11X1 T14 03 arithmetic & geometric means (2010)
•
1 like•1,699 views
The document defines the arithmetic mean and geometric mean. The arithmetic mean is calculated by adding all values and dividing by the total number of values. The geometric mean is calculated by multiplying all values and taking the nth root of the product, where n is the number of values. An example is provided to find the arithmetic mean and geometric mean of the values 4 and 25.
Report
Share
Report
Share
Download to read offline
Recommended
Belief in prophets
Belief in prophetsQuaid-e-Awam University of Engineering, Science and Technology, Nawabshah, Sindh, Pakistan
This slides will help you in studying fundamentals of Islam.Follow me for more slide notes . these slides are to the point.Properties of triangles
1) The document discusses geometry concepts related to angles of triangles including the triangle angle sum theorem, exterior angle theorem, and finding measures of unknown angles using known information.
2) Key details include that the sum of the interior angles of any triangle is 180 degrees, and the measure of an exterior angle is equal to the sum of the remote interior angles.
3) Examples are provided to demonstrate using these theorems to find the measures of missing angles in different triangle scenarios.
Compilation of the qur'an
The Qur'an was first compiled during the caliphate of Abu Bakr after the Prophet Muhammad's death. Zayed Ibn Thabit was tasked with collecting the Qur'an from fragments on parchment and the memories of companions who had memorized it. This early compilation was kept with Hafsa, daughter of Umar. Later, during the caliphate of Uthman, several copies were made and sent to various Muslim communities to avoid variations in recitation. A system of dots and diacritical marks was gradually added over the next centuries to preserve the Qur'an's text.
Kungfu math p3 slide16 (angles)pdf
This document provides information about basic angles including:
- An angle measures the amount of turn
- There are different names for angles depending on their measure including acute (less than 90 degrees), right (90 degrees), obtuse (greater than 90 but less than 180 degrees), straight (180 degrees), and reflex (greater than 180 degrees)
- Examples are given of identifying right angles, angles greater than 90 degrees, and angles smaller than 90 degrees in 2D figures
Women In Islam
The document discusses the status and treatment of women in different societies throughout history and how Islam improved women's rights and status. It notes that before Islam, women in places like Arabia were often mistreated, having no rights and facing practices like female infanticide. It then outlines various rights and roles for women established in Islam, including rights to education, inheritance, divorce, and not being forced to marry. The document emphasizes that men and women are seen as equal in Islam while having different responsibilities. It also discusses polygamy, marriage, and divorce practices in Islamic law.
Introduction To Hadith
The document provides an introduction to Hadith, including:
1) Definitions of Hadith, both literal and technical, and the subject matter of Hadith, which is to obtain guidance from the Prophet Muhammad.
2) The aims and objectives of studying Hadith are to follow the guidance of the Prophet in order to be successful in this life and the next.
3) Hadith is mentioned in the Quran referring to the guidance given to the Prophet by Allah, establishing the authority of Hadith from the Quran itself.
Team work islamic perspective
Team Definition
Quran & Hadith On Team Work
Types Of Teams
Advantages Of Team Work
Characteristics Of Effective Team
Symptoms Of Poor Teamwork
Stages Of Team Work
Diseases That Destroy Teams
Women's rights in islam
Islam affords women extensive rights and empowerment not found in other religions or philosophies. Specifically:
1. Muslim women have the right to education, independent property, work or business to earn their own money, equal reward for equal work, expressing opinions and advocating causes.
2. Additional rights include provisions from husbands, negotiating marriage terms, divorce, keeping their own money, sexual satisfaction from husbands, child custody after divorce, choosing and refusing husbands, and remarrying.
3. Exceptions are made for fasting, praying, and congregational attendance during menstruation and post-childbirth bleeding, but women are otherwise allowed to do what men do and have historically governed Islamic provinces and states
Recommended
Belief in prophets
Belief in prophetsQuaid-e-Awam University of Engineering, Science and Technology, Nawabshah, Sindh, Pakistan
This slides will help you in studying fundamentals of Islam.Follow me for more slide notes . these slides are to the point.Properties of triangles
1) The document discusses geometry concepts related to angles of triangles including the triangle angle sum theorem, exterior angle theorem, and finding measures of unknown angles using known information.
2) Key details include that the sum of the interior angles of any triangle is 180 degrees, and the measure of an exterior angle is equal to the sum of the remote interior angles.
3) Examples are provided to demonstrate using these theorems to find the measures of missing angles in different triangle scenarios.
Compilation of the qur'an
The Qur'an was first compiled during the caliphate of Abu Bakr after the Prophet Muhammad's death. Zayed Ibn Thabit was tasked with collecting the Qur'an from fragments on parchment and the memories of companions who had memorized it. This early compilation was kept with Hafsa, daughter of Umar. Later, during the caliphate of Uthman, several copies were made and sent to various Muslim communities to avoid variations in recitation. A system of dots and diacritical marks was gradually added over the next centuries to preserve the Qur'an's text.
Kungfu math p3 slide16 (angles)pdf
This document provides information about basic angles including:
- An angle measures the amount of turn
- There are different names for angles depending on their measure including acute (less than 90 degrees), right (90 degrees), obtuse (greater than 90 but less than 180 degrees), straight (180 degrees), and reflex (greater than 180 degrees)
- Examples are given of identifying right angles, angles greater than 90 degrees, and angles smaller than 90 degrees in 2D figures
Women In Islam
The document discusses the status and treatment of women in different societies throughout history and how Islam improved women's rights and status. It notes that before Islam, women in places like Arabia were often mistreated, having no rights and facing practices like female infanticide. It then outlines various rights and roles for women established in Islam, including rights to education, inheritance, divorce, and not being forced to marry. The document emphasizes that men and women are seen as equal in Islam while having different responsibilities. It also discusses polygamy, marriage, and divorce practices in Islamic law.
Introduction To Hadith
The document provides an introduction to Hadith, including:
1) Definitions of Hadith, both literal and technical, and the subject matter of Hadith, which is to obtain guidance from the Prophet Muhammad.
2) The aims and objectives of studying Hadith are to follow the guidance of the Prophet in order to be successful in this life and the next.
3) Hadith is mentioned in the Quran referring to the guidance given to the Prophet by Allah, establishing the authority of Hadith from the Quran itself.
Team work islamic perspective
Team Definition
Quran & Hadith On Team Work
Types Of Teams
Advantages Of Team Work
Characteristics Of Effective Team
Symptoms Of Poor Teamwork
Stages Of Team Work
Diseases That Destroy Teams
Women's rights in islam
Islam affords women extensive rights and empowerment not found in other religions or philosophies. Specifically:
1. Muslim women have the right to education, independent property, work or business to earn their own money, equal reward for equal work, expressing opinions and advocating causes.
2. Additional rights include provisions from husbands, negotiating marriage terms, divorce, keeping their own money, sexual satisfaction from husbands, child custody after divorce, choosing and refusing husbands, and remarrying.
3. Exceptions are made for fasting, praying, and congregational attendance during menstruation and post-childbirth bleeding, but women are otherwise allowed to do what men do and have historically governed Islamic provinces and states
Prophet Muhammad (saw) -blessing for mankind
The document provides a summary of the life of the Prophet Muhammad (peace be upon him) in 3 parts:
1) It describes his birth and early life as an orphan in Makkah, his work as a merchant, and his marriage to Khadijah.
2) It discusses his receiving of the first revelation from Gabriel at age 40 and his 23 years of receiving revelations that were later compiled into the Quran. He faced challenges from Makkan leaders as he spread the message of Islam.
3) It outlines some key later events including his migration to Madinah to escape persecution, treatments of envoys in Madinah, the liberation of Makkah, and his farewell
Numbers in Arabic
🌟 Learn Arabic & Qur'an online 🌟
Al-Andalus Academy for Arabic & Qur'an online studies
Enjoy learning Arabic & Qur'an in a different, simple, and professional way
✅ https://Al-AndalusAcademy.com
6 Figure Grid References
The document discusses 6 figure grid references, which provide more precise locations than 4 figure grid references by dividing grid squares into tenths. It explains that the first 3 figures indicate easting and the second 3 indicate northing. Several examples are given of determining 6 figure grid references from maps and vice versa. The reader is then prompted to answer practice questions to test their understanding.
Basic arabic grammar
This document provides an introduction to and overview of the first chapter of the textbook "Basic Arabic Grammar: Part A". The chapter focuses on forming basic nominal sentences in Arabic. It discusses definite and indefinite nouns and adjectives, and how they are used in nominal sentences of the form "subject is/are predicate". It also introduces the singular detached pronouns that can replace nouns as subjects, and the conjunction "and" which can join multiple predicates or nominal sentences. Several example sentences are provided to illustrate these concepts.
Parents Rights in Islam
This document discusses the importance of kindness towards parents in Islam through several hadiths and quotes from the Quran. The main points are:
1) The Prophet Muhammad said that goodness towards parents is the greatest obligatory act, and one of the best deeds is performing prayers on time and being good to parents.
2) Allah says in a hadith that if a disobedient child comes to Him with all the good deeds of the prophets, He will not accept them due to their disobedience to parents.
3) Islam emphasizes the rights of parents strongly because parental love and care for children is instinctual, while children's love for parents tends to lessen when they are grown,
The Present tense in Modern Standard Arabic
Learn Arabic with Arabeya Arabic Language Center
Follow us on :
www.Arabeya.org
Arabic Grammar
The document provides an overview of Tajweed, which is the rules of recitation of the Qur'an. It discusses Arabic alphabets and pronunciation, symbols used in recitation, and the different chapters of the Qur'an. It also summarizes key aspects of Arabic grammar including the different parts of a meaningful word (noun, verb, preposition), types of nouns (gender, number), and pronouns. Additionally, it covers topics like vowels, sun and moon letters, and prepositions. The document thus serves as a comprehensive introduction to the principles and structure of both Qur'anic recitation and Arabic grammar.
Islamic Ethics : An Introduction
This document outlines the course for Islamic Ethics. It begins by defining ethics and distinguishing it from morality. It then discusses the scope and importance of Islamic ethics, as well as its sources which include the Quran, hadith, theology, philosophy, mysticism, and jurisprudence. It also examines the relationship between ethics and religion, comparing religious morality to secular morality. Specifically, it looks at the ultimate end of human conduct, knowledge of good and evil, and sanction behind moral law from a secular perspective.
Introduction to islamic law
Islamic law, known as Sharia, is derived from two primary sources - the Quran and the Sunnah (traditions and sayings of the prophet Muhammad). It covers both religious and secular matters of law. There are two secondary sources - ijma, which is scholarly consensus, and qiyas, which is analogical reasoning or derivation of rulings through analogy. Sharia is interpreted by Islamic legal scholars and judges and applies different concepts of crime, justice and punishment than secular law. It has evolved over time through the work of early Muslim jurists and scholars.
Al qaza
A Qazi is a religious judge in Islam who works under Sharia law. A Qazi may be appointed by an Imam, Caliph, Sultan, or governor if given the authority. According to Hidaya, a book of Islamic jurisprudence, a Qazi must be a Muslim, adult, free man who has basic knowledge of Islamic law and acts with impartiality and integrity. Additional qualifications include producing decisions in writing, maintaining equality, and having knowledge of principles of justice and rules of interpretation.
27 SHORT ARABIC PHRASES pdf.
The document lists various Arabic terms used to indicate or reference different points in time, including:
- In the near future/next year/next month to refer to upcoming times.
- A long time ago/in the past to refer to distant past times.
- At the same time/at that time to refer to simultaneous or concurrent times.
- Last week/last month/last year to refer to recent past times within the past week, month or year.
- Within an hour/this morning/these days/few moments ago to refer to very recent times.
- After tomorrow/before one hour/recently to refer to times relative to the present or near future.
Hamidullah work .pdf
This document provides a biography of Muhammad Hamidullah, focusing on his early life, education, and career. Some key points:
- Hamidullah was born in 1908 in Hyderabad, India to a family with scholarly ancestry. He received early religious education and excelled academically.
- He earned multiple advanced degrees, including a PhD from the University of Bonn in 1933 on the topic of neutrality in Islamic international law. He later earned a doctorate from the Sorbonne in 1935.
- Hamidullah had an illustrious teaching and research career, holding positions at universities in Germany, India, and France. He wrote extensively on topics related to Islamic law, theology,
Congruent and Similar Polygons
Congruent polygons have exactly the same side and angle measurements, making them identical in size and shape. Similar polygons have the same shape but may differ in size, with their corresponding sides being proportional by a scale factor. Examples demonstrate congruent triangles with the same measurements as well as similar quadrilaterals where one has sides twice the length of the other.
Angles
An angle is formed by two lines or rays diverging from a common point called the vertex. There are several types of angles including acute, right, obtuse, straight, and reflex angles defined by their degree measurements. The parts of an angle include the vertex, two arms, and degrees. Angles can be named using the less than symbol followed by three letters to indicate the vertex points.
Lesson 2 | Parts of Speech - 1 | Learn Arabic to Understand the Quran for Allaah
Learn Arabic to Understand the Quran for Allah: New Lessons Monday - Friday, Live Classes on Saturdays and Sunday! Free Online Course.
Jihad
Jihad refers to the struggle to live out the Muslim faith fully and promote virtue. There are three main types: the internal struggle against sin; the struggle to build a just society; and armed defense of Islam if necessary. Jihad becomes compulsory when Muslim lives, religion or lands are under threat, and is subject to strict rules about protecting non-combatants and showing mercy to prisoners according to Islamic scripture and teachings.
Seerah of Prophet Muhammad (S)--Meccan Period
This document provides an overview of the life of Prophet Muhammad during the Meccan period. It describes the political and religious situation at the time, the advantages of preaching to Arabs, difficulties faced, stages of the early Islamic movement including secret preaching, open preaching, persecution, and extreme oppression. It also discusses the Prophet's migration from Mecca to Medina and his arrival in Medina.
The rule of qiyas its meaning, justification, types, scope, application, feas...
Qiyas, Definition of Qiyas, Scope of Qiyas, Meaning of Qiyas,
Applictaion of Qiyas, Types of Qiyas, examples of qiyas,
define qiyas with different examples
Madinah Arabic Reader Book1
The document provides an introduction to an 8-book Arabic language series developed for students from kindergarten through 8th grade at the Nur-UI-Islam Academy, an Islamic school in Florida. It was created by Professor Abdur Rahim, former professor of Arabic at the Islamic University of Madinah, at the request of the Academy's Board of Directors. The series aims to teach students to read, write and speak Arabic with proficiency by 8th grade using a classical grammatical approach through conversations and exercises in each lesson. It is currently being used at the Academy to prepare students for London GCE Ordinary and Advanced Level Arabic examinations. The Board and community are grateful to Professor Rahim for his work developing the
Goodbye slideshare UPDATE
Slideshare is discontinuing its Slidecast feature as of February 28, 2014. Existing Slidecasts will be converted to static presentations without audio by April 30, 2014. The document informs users that new slidecasts can be found on myPlick.com or the author's blog starting in 2014. However, myPlick proved unreliable, so future slidecasts will instead be hosted on the author's YouTube channel.
Goodbye slideshare
NOTE: there is no sound, i.e. it is not a slidecast, as slideshare are going to get rid of this feature.
More Related Content
What's hot
Prophet Muhammad (saw) -blessing for mankind
The document provides a summary of the life of the Prophet Muhammad (peace be upon him) in 3 parts:
1) It describes his birth and early life as an orphan in Makkah, his work as a merchant, and his marriage to Khadijah.
2) It discusses his receiving of the first revelation from Gabriel at age 40 and his 23 years of receiving revelations that were later compiled into the Quran. He faced challenges from Makkan leaders as he spread the message of Islam.
3) It outlines some key later events including his migration to Madinah to escape persecution, treatments of envoys in Madinah, the liberation of Makkah, and his farewell
Numbers in Arabic
🌟 Learn Arabic & Qur'an online 🌟
Al-Andalus Academy for Arabic & Qur'an online studies
Enjoy learning Arabic & Qur'an in a different, simple, and professional way
✅ https://Al-AndalusAcademy.com
6 Figure Grid References
The document discusses 6 figure grid references, which provide more precise locations than 4 figure grid references by dividing grid squares into tenths. It explains that the first 3 figures indicate easting and the second 3 indicate northing. Several examples are given of determining 6 figure grid references from maps and vice versa. The reader is then prompted to answer practice questions to test their understanding.
Basic arabic grammar
This document provides an introduction to and overview of the first chapter of the textbook "Basic Arabic Grammar: Part A". The chapter focuses on forming basic nominal sentences in Arabic. It discusses definite and indefinite nouns and adjectives, and how they are used in nominal sentences of the form "subject is/are predicate". It also introduces the singular detached pronouns that can replace nouns as subjects, and the conjunction "and" which can join multiple predicates or nominal sentences. Several example sentences are provided to illustrate these concepts.
Parents Rights in Islam
This document discusses the importance of kindness towards parents in Islam through several hadiths and quotes from the Quran. The main points are:
1) The Prophet Muhammad said that goodness towards parents is the greatest obligatory act, and one of the best deeds is performing prayers on time and being good to parents.
2) Allah says in a hadith that if a disobedient child comes to Him with all the good deeds of the prophets, He will not accept them due to their disobedience to parents.
3) Islam emphasizes the rights of parents strongly because parental love and care for children is instinctual, while children's love for parents tends to lessen when they are grown,
The Present tense in Modern Standard Arabic
Learn Arabic with Arabeya Arabic Language Center
Follow us on :
www.Arabeya.org
Arabic Grammar
The document provides an overview of Tajweed, which is the rules of recitation of the Qur'an. It discusses Arabic alphabets and pronunciation, symbols used in recitation, and the different chapters of the Qur'an. It also summarizes key aspects of Arabic grammar including the different parts of a meaningful word (noun, verb, preposition), types of nouns (gender, number), and pronouns. Additionally, it covers topics like vowels, sun and moon letters, and prepositions. The document thus serves as a comprehensive introduction to the principles and structure of both Qur'anic recitation and Arabic grammar.
Islamic Ethics : An Introduction
This document outlines the course for Islamic Ethics. It begins by defining ethics and distinguishing it from morality. It then discusses the scope and importance of Islamic ethics, as well as its sources which include the Quran, hadith, theology, philosophy, mysticism, and jurisprudence. It also examines the relationship between ethics and religion, comparing religious morality to secular morality. Specifically, it looks at the ultimate end of human conduct, knowledge of good and evil, and sanction behind moral law from a secular perspective.
Introduction to islamic law
Islamic law, known as Sharia, is derived from two primary sources - the Quran and the Sunnah (traditions and sayings of the prophet Muhammad). It covers both religious and secular matters of law. There are two secondary sources - ijma, which is scholarly consensus, and qiyas, which is analogical reasoning or derivation of rulings through analogy. Sharia is interpreted by Islamic legal scholars and judges and applies different concepts of crime, justice and punishment than secular law. It has evolved over time through the work of early Muslim jurists and scholars.
Al qaza
A Qazi is a religious judge in Islam who works under Sharia law. A Qazi may be appointed by an Imam, Caliph, Sultan, or governor if given the authority. According to Hidaya, a book of Islamic jurisprudence, a Qazi must be a Muslim, adult, free man who has basic knowledge of Islamic law and acts with impartiality and integrity. Additional qualifications include producing decisions in writing, maintaining equality, and having knowledge of principles of justice and rules of interpretation.
27 SHORT ARABIC PHRASES pdf.
The document lists various Arabic terms used to indicate or reference different points in time, including:
- In the near future/next year/next month to refer to upcoming times.
- A long time ago/in the past to refer to distant past times.
- At the same time/at that time to refer to simultaneous or concurrent times.
- Last week/last month/last year to refer to recent past times within the past week, month or year.
- Within an hour/this morning/these days/few moments ago to refer to very recent times.
- After tomorrow/before one hour/recently to refer to times relative to the present or near future.
Hamidullah work .pdf
This document provides a biography of Muhammad Hamidullah, focusing on his early life, education, and career. Some key points:
- Hamidullah was born in 1908 in Hyderabad, India to a family with scholarly ancestry. He received early religious education and excelled academically.
- He earned multiple advanced degrees, including a PhD from the University of Bonn in 1933 on the topic of neutrality in Islamic international law. He later earned a doctorate from the Sorbonne in 1935.
- Hamidullah had an illustrious teaching and research career, holding positions at universities in Germany, India, and France. He wrote extensively on topics related to Islamic law, theology,
Congruent and Similar Polygons
Congruent polygons have exactly the same side and angle measurements, making them identical in size and shape. Similar polygons have the same shape but may differ in size, with their corresponding sides being proportional by a scale factor. Examples demonstrate congruent triangles with the same measurements as well as similar quadrilaterals where one has sides twice the length of the other.
Angles
An angle is formed by two lines or rays diverging from a common point called the vertex. There are several types of angles including acute, right, obtuse, straight, and reflex angles defined by their degree measurements. The parts of an angle include the vertex, two arms, and degrees. Angles can be named using the less than symbol followed by three letters to indicate the vertex points.
Lesson 2 | Parts of Speech - 1 | Learn Arabic to Understand the Quran for Allaah
Learn Arabic to Understand the Quran for Allah: New Lessons Monday - Friday, Live Classes on Saturdays and Sunday! Free Online Course.
Jihad
Jihad refers to the struggle to live out the Muslim faith fully and promote virtue. There are three main types: the internal struggle against sin; the struggle to build a just society; and armed defense of Islam if necessary. Jihad becomes compulsory when Muslim lives, religion or lands are under threat, and is subject to strict rules about protecting non-combatants and showing mercy to prisoners according to Islamic scripture and teachings.
Seerah of Prophet Muhammad (S)--Meccan Period
This document provides an overview of the life of Prophet Muhammad during the Meccan period. It describes the political and religious situation at the time, the advantages of preaching to Arabs, difficulties faced, stages of the early Islamic movement including secret preaching, open preaching, persecution, and extreme oppression. It also discusses the Prophet's migration from Mecca to Medina and his arrival in Medina.
The rule of qiyas its meaning, justification, types, scope, application, feas...
Qiyas, Definition of Qiyas, Scope of Qiyas, Meaning of Qiyas,
Applictaion of Qiyas, Types of Qiyas, examples of qiyas,
define qiyas with different examples
Madinah Arabic Reader Book1
The document provides an introduction to an 8-book Arabic language series developed for students from kindergarten through 8th grade at the Nur-UI-Islam Academy, an Islamic school in Florida. It was created by Professor Abdur Rahim, former professor of Arabic at the Islamic University of Madinah, at the request of the Academy's Board of Directors. The series aims to teach students to read, write and speak Arabic with proficiency by 8th grade using a classical grammatical approach through conversations and exercises in each lesson. It is currently being used at the Academy to prepare students for London GCE Ordinary and Advanced Level Arabic examinations. The Board and community are grateful to Professor Rahim for his work developing the
What's hot (20)
Lesson 2 | Parts of Speech - 1 | Learn Arabic to Understand the Quran for Allaah
Lesson 2 | Parts of Speech - 1 | Learn Arabic to Understand the Quran for Allaah
The rule of qiyas its meaning, justification, types, scope, application, feas...
The rule of qiyas its meaning, justification, types, scope, application, feas...
More from Nigel Simmons
Goodbye slideshare UPDATE
Slideshare is discontinuing its Slidecast feature as of February 28, 2014. Existing Slidecasts will be converted to static presentations without audio by April 30, 2014. The document informs users that new slidecasts can be found on myPlick.com or the author's blog starting in 2014. However, myPlick proved unreliable, so future slidecasts will instead be hosted on the author's YouTube channel.
Goodbye slideshare
NOTE: there is no sound, i.e. it is not a slidecast, as slideshare are going to get rid of this feature.
11 x1 t01 03 factorising (2014)
The document discusses different methods for factorising expressions:
1) Looking for a common factor and dividing it out of all terms
2) Using the difference of two squares formula (a2 - b2 = (a - b)(a + b))
3) Factorising quadratic trinomials into two binomial factors by identifying the values that multiply to give the constant term and sum to give the coefficient of the linear term.
11 x1 t01 01 algebra & indices (2014)
The document provides information on index laws and the meaning of indices in algebra:
- Index laws state that am × an = am+n, am ÷ an = am-n, and (am)n = amn. Exponents can be added or subtracted when multiplying or dividing terms with the same base.
- Positive exponents indicate a term is raised to a power. Negative exponents indicate a root is being taken. Terms with exponents are evaluated from left to right.
- Examples demonstrate how to simplify expressions using index laws and interpret different types of indices.
12 x1 t01 03 integrating derivative on function (2013)
The document discusses integrating derivatives of functions. It states that the integral of the derivative of a function f(x) is equal to the natural log of f(x) plus a constant. It then provides examples of integrating several derivatives: (i) ∫(1/(7-3x)) dx = -1/3 log(7-3x) + c, (ii) ∫(1/(8x+5)) dx = 1/8 log(8x+5) + c, and (iii) ∫(x5/(x-2)) dx = 1/6 log(x6-2) + c. It also discusses techniques for integrating fractions by polynomial long division and finds
12 x1 t01 01 log laws (2013)
The document discusses logarithms and their properties. Logarithms are defined as the inverse of exponentials. If y = ax, then x = loga y. The natural logarithm is log base e, written as ln. Properties of logarithms include: loga m + loga n = loga mn; loga m - loga n = loga(m/n); loga mn = n loga m; loga 1 = 0; loga a = 1. Examples of evaluating logarithmic expressions are provided.
X2 t02 03 roots & coefficients (2013)
The document discusses relationships between the coefficients and roots of polynomials. It states that for a polynomial P(x) = axn + bxn-1 + cxn-2 + ..., the sum of the roots equals -b/a, the sum of the roots taken two at a time equals c/a, and so on for higher order terms. It also provides examples of using these relationships to find the sums of roots for a given polynomial.
X2 t02 02 multiple roots (2013)
P
4
3
2
The document discusses properties of polynomials with multiple roots. It first proves that if a polynomial P(x) has a root x = a of multiplicity m, then the derivative of P(x), P'(x), will have a root x = a of multiplicity m-1. It then provides an example of solving a cubic equation given it has a double root. Finally, it examines a quartic polynomial and shows that its root α cannot be 0, 1, or -1, and that 1/
X2 t02 01 factorising complex expressions (2013)
The document discusses factorizing complex expressions. The main points are:
- If a polynomial's coefficients are real, its roots will appear in complex conjugate pairs.
- Any polynomial of degree n can be factorized into a mixture of quadratic and linear factors over real numbers, or into n linear factors over complex numbers.
- Odd degree polynomials must have at least one real root.
- Examples of factorizing polynomials over both real and complex numbers are provided.
11 x1 t16 07 approximations (2013)
The document describes the Trapezoidal Rule for approximating the area under a curve between two points. It shows that the area A is estimated by dividing the region into trapezoids with height equal to the function values at the interval endpoints and bases equal to the intervals. In general, the area is approximated as the sum of the areas of each trapezoid, which is equal to the average of the endpoint function values multiplied by the interval length.
11 x1 t16 05 volumes (2013)
The document discusses methods for calculating the volumes of solids of revolution. It provides formulas for finding volumes when an area is revolved around either the x-axis or y-axis. Examples are given for finding volumes of common solids like cones, spheres, and others. Steps are shown for using the formulas to calculate volumes based on given functions and limits of revolution.
11 x1 t16 04 areas (2013)
The document discusses different methods for calculating the area under a curve or between curves.
(1) The area below the x-axis is given by the integral of the function between the bounds, which can be positive or negative depending on whether the area is above or below the x-axis.
(2) To calculate the area on the y-axis, the function is solved for x in terms of y, then the bounds are substituted into the integral of this new function with respect to y.
(3) The area between two curves is calculated by taking the integral of the upper curve minus the integral of the lower curve, both between the same bounds on the x-axis.
11 x1 t16 02 definite integral (2013)
The document discusses 8 properties of definite integrals:
1) Integrating polynomials results in a fraction.
2) Constants can be factored out of integrals.
3) Integrals of sums are equal to the sum of integrals.
4) Splitting an integral range results in the sum of the integrals.
5) Integrals of positive functions over a range are positive, and negative if the function is negative.
6) Integrals can be compared based on the relative values of the integrands.
7) Changing the limits of integration flips the sign of the integral.
8) Integrals of odd functions over a symmetric range are zero, and integrals of even functions are twice the integral over
More from Nigel Simmons (20)
12 x1 t01 03 integrating derivative on function (2013)
12 x1 t01 03 integrating derivative on function (2013)
Recently uploaded
Benner "Expanding Pathways to Publishing Careers"
This presentation was provided by Rebecca Benner, Ph.D., of the American Society of Anesthesiologists, for the second session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session Two: 'Expanding Pathways to Publishing Careers,' was held June 13, 2024.
BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 9 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2024-2025 - ...
BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 9 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2024-2025 - ...Nguyen Thanh Tu Collection
https://app.box.com/s/tacvl9ekroe9hqupdnjruiypvm9rdaneRHEOLOGY Physical pharmaceutics-II notes for B.pharm 4th sem students
Physical pharmaceutics notes for B.pharm students
Educational Technology in the Health Sciences
Plenary presentation at the NTTC Inter-university Workshop, 18 June 2024, Manila Prince Hotel.
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Aberdeen
Elevate Your Nonprofit's Online Presence_ A Guide to Effective SEO Strategies...
Whether you're new to SEO or looking to refine your existing strategies, this webinar will provide you with actionable insights and practical tips to elevate your nonprofit's online presence.
HYPERTENSION - SLIDE SHARE PRESENTATION.
IT WILL BE HELPFULL FOR THE NUSING STUDENTS
IT FOCUSED ON MEDICAL MANAGEMENT AND NURSING MANAGEMENT.
HIGHLIGHTS ON HEALTH EDUCATION.
BIOLOGY NATIONAL EXAMINATION COUNCIL (NECO) 2024 PRACTICAL MANUAL.pptx
Practical manual for National Examination Council, Nigeria.
Contains guides on answering questions on the specimens provided
How to deliver Powerpoint Presentations.pptx
"How to make and deliver dynamic presentations by making it more interactive to captivate your audience attention"
THE SACRIFICE HOW PRO-PALESTINE PROTESTS STUDENTS ARE SACRIFICING TO CHANGE T...
The recent surge in pro-Palestine student activism has prompted significant responses from universities, ranging from negotiations and divestment commitments to increased transparency about investments in companies supporting the war on Gaza. This activism has led to the cessation of student encampments but also highlighted the substantial sacrifices made by students, including academic disruptions and personal risks. The primary drivers of these protests are poor university administration, lack of transparency, and inadequate communication between officials and students. This study examines the profound emotional, psychological, and professional impacts on students engaged in pro-Palestine protests, focusing on Generation Z's (Gen-Z) activism dynamics. This paper explores the significant sacrifices made by these students and even the professors supporting the pro-Palestine movement, with a focus on recent global movements. Through an in-depth analysis of printed and electronic media, the study examines the impacts of these sacrifices on the academic and personal lives of those involved. The paper highlights examples from various universities, demonstrating student activism's long-term and short-term effects, including disciplinary actions, social backlash, and career implications. The researchers also explore the broader implications of student sacrifices. The findings reveal that these sacrifices are driven by a profound commitment to justice and human rights, and are influenced by the increasing availability of information, peer interactions, and personal convictions. The study also discusses the broader implications of this activism, comparing it to historical precedents and assessing its potential to influence policy and public opinion. The emotional and psychological toll on student activists is significant, but their sense of purpose and community support mitigates some of these challenges. However, the researchers call for acknowledging the broader Impact of these sacrifices on the future global movement of FreePalestine.
Recently uploaded (20)
BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 9 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2024-2025 - ...
BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 9 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2024-2025 - ...
RHEOLOGY Physical pharmaceutics-II notes for B.pharm 4th sem students
RHEOLOGY Physical pharmaceutics-II notes for B.pharm 4th sem students
SWOT analysis in the project Keeping the Memory @live.pptx
SWOT analysis in the project Keeping the Memory @live.pptx
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
Elevate Your Nonprofit's Online Presence_ A Guide to Effective SEO Strategies...
Elevate Your Nonprofit's Online Presence_ A Guide to Effective SEO Strategies...
BIOLOGY NATIONAL EXAMINATION COUNCIL (NECO) 2024 PRACTICAL MANUAL.pptx
BIOLOGY NATIONAL EXAMINATION COUNCIL (NECO) 2024 PRACTICAL MANUAL.pptx
Juneteenth Freedom Day 2024 David Douglas School District
Juneteenth Freedom Day 2024 David Douglas School District
THE SACRIFICE HOW PRO-PALESTINE PROTESTS STUDENTS ARE SACRIFICING TO CHANGE T...
THE SACRIFICE HOW PRO-PALESTINE PROTESTS STUDENTS ARE SACRIFICING TO CHANGE T...
REASIGNACION 2024 UGEL CHUPACA 2024 UGEL CHUPACA.pdf
REASIGNACION 2024 UGEL CHUPACA 2024 UGEL CHUPACA.pdf
11X1 T14 03 arithmetic & geometric means (2010)
- 1. Arithmetic & Geometric Means
- 2. Arithmetic & Geometric Means Arithmetic Mean(average) a1 a2 a3 an AM n
- 3. Arithmetic & Geometric Means Arithmetic Mean(average) a1 a2 a3 an AM n Geometric Mean GM n a1a2 a3 an
- 4. Arithmetic & Geometric Means Arithmetic Mean(average) a1 a2 a3 an AM n Geometric Mean GM n a1a2 a3 an e.g.Find the AM and GM of 4 and 25
- 5. Arithmetic & Geometric Means Arithmetic Mean(average) a1 a2 a3 an AM n Geometric Mean GM n a1a2 a3 an e.g.Find the AM and GM of 4 and 25 25 4 AM 2 29 2
- 6. Arithmetic & Geometric Means Arithmetic Mean(average) a1 a2 a3 an AM n Geometric Mean GM n a1a2 a3 an e.g.Find the AM and GM of 4 and 25 25 4 AM GM 25 4 2 100 29 10 2
- 7. Exercise 6F; 1ace etc, 2bd, 4, 7, 8ade, 10, 13, 19*