1. Find the equation of tangent to the curve x = sin 3t, y = cos 2t at t = π/4.
2. Solve the differential equation cos2x dy/dx + y = tan x.
3. Using integration, find the area of the region bounded by the parabola y2 = 4x and the circle 4x2 + 4y2 = 9.
The following presentation is an introduction to the Algebraic Methods – part one for level 4 Mathematics. This resources is a part of the 2009/2010 Engineering (foundation degree, BEng and HN) courses from University of Wales Newport (course codes H101, H691, H620, HH37 and 001H). This resource is a part of the core modules for the full time 1st year undergraduate programme.
The BEng & Foundation Degrees and HNC/D in Engineering are designed to meet the needs of employers by placing the emphasis on the theoretical, practical and vocational aspects of engineering within the workplace and beyond. Engineering is becoming more high profile, and therefore more in demand as a skill set, in today’s high-tech world. This course has been designed to provide you with knowledge, skills and practical experience encountered in everyday engineering environments.
The following presentation is an introduction to the Algebraic Methods – part one for level 4 Mathematics. This resources is a part of the 2009/2010 Engineering (foundation degree, BEng and HN) courses from University of Wales Newport (course codes H101, H691, H620, HH37 and 001H). This resource is a part of the core modules for the full time 1st year undergraduate programme.
The BEng & Foundation Degrees and HNC/D in Engineering are designed to meet the needs of employers by placing the emphasis on the theoretical, practical and vocational aspects of engineering within the workplace and beyond. Engineering is becoming more high profile, and therefore more in demand as a skill set, in today’s high-tech world. This course has been designed to provide you with knowledge, skills and practical experience encountered in everyday engineering environments.
II PUC (MATHEMATICS) ANNUAL MODEL QUESTION PAPER FOR ALL SCIENCE STUDENTS WHO...Bagalkot
My dear Students,
Wishing you all happy SHIVRATRI. & ALL THE BEST IN YOUR ANNUAL EXAMS-2014
Here I have uploaded II- P.U.C MATHEMATICS MODEL QUESTION PAPER FOR the year 2014 Which i have designed according to New syllabus of CBSE. I hope this model paper will be helpful to all the students who are writing annual exams on 18-March-2014.
wish you all the best
Regards,
A. NAGARAJ
Director-Faculty
Shree Susheela Tutorials
BAGALKOT-587101
mob: 9845222682
In pursuit of excellence, the CBSE board conducts a thorough research on emerging educational requirements. While designing the syllabus, the board ensures that every topic meets the learning needs of students in the best possible manner. CBSE Class 12 Maths - http://cbse.edurite.com/cbse-maths/cbse-class-12-maths.html
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
Biological screening of herbal drugs: Introduction and Need for
Phyto-Pharmacological Screening, New Strategies for evaluating
Natural Products, In vitro evaluation techniques for Antioxidants, Antimicrobial and Anticancer drugs. In vivo evaluation techniques
for Anti-inflammatory, Antiulcer, Anticancer, Wound healing, Antidiabetic, Hepatoprotective, Cardio protective, Diuretics and
Antifertility, Toxicity studies as per OECD guidelines
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
Acetabularia Information For Class 9 .docxvaibhavrinwa19
Acetabularia acetabulum is a single-celled green alga that in its vegetative state is morphologically differentiated into a basal rhizoid and an axially elongated stalk, which bears whorls of branching hairs. The single diploid nucleus resides in the rhizoid.
Francesca Gottschalk - How can education support child empowerment.pptxEduSkills OECD
Francesca Gottschalk from the OECD’s Centre for Educational Research and Innovation presents at the Ask an Expert Webinar: How can education support child empowerment?
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
1. CLASS XII ASSIGNMENT (CHAPTERS 1 TO 9)
1. Find the equation of tangent to the curve x = sin 3t , y = cos 2t, at t =
𝜋
4
.
2. Solve the following differential equation: cos2
x
𝑑𝑦
𝑑𝑥
+ y = tan x.
3. Using integration, find the area of the region bounded by the parabola y2
= 4x and the circle 4x2
+ 4y2
= 9.
4. Evaluate : ∫ √
𝑎−𝑥
𝑎+𝑥
𝑎
−𝑎
dx .
5. By using properties of determinants, prove the following: |
𝑥 + 4 2𝑥 2𝑥
2𝑥 𝑥 + 4 2𝑥
2𝑥 2𝑥 𝑥 + 4
| = (5x + 4) (4 – x)2
.
6. Evaluate : ∫
𝑒 𝑥
√5−4𝑒 𝑥−𝑒2𝑥
dx.
7. If y = 3 cos (log x) + 4 sin (log x), then show that x2 𝑑2
𝑦
𝑑𝑥2 + x
𝑑𝑦
𝑑𝑥
+ y = 0.
8. Using matrices, solve the following system of equations : 2x – 3y + 5z = 11 ; 3x + 2y – 4z = -5 ; x + y – 2z = -3.
9. Evaluate : ∫
𝑒𝑐𝑜𝑠 𝑥
𝑒𝑐𝑜𝑠 𝑥+ 𝑒− 𝑐𝑜𝑠 𝑥
𝜋
0
dx.
10. Let Z be the set of all integers and R be the relation on Z defined as
R = {(a, b) : a, b ∈ Z, and (a – b) is divisible by 5}. Prove that R is an equivalence relation.
11. Evaluate : ∫
𝑠𝑖𝑛𝑥+𝑐𝑜𝑠𝑥
√ 𝑠𝑖𝑛 2𝑥
𝜋
3
𝜋
6
𝑑𝑥.
12. Using integration, find the area of the region bounded by the curve x2
= 4y and the line x = 4y – 2.
13. Show that the right circular cylinder, open at the top, and of given surface area and maximum volume
is such that its height is equal to the radius of the base.
14. Consider the binary operation * on the set {1, 2, 3, 4, 5} defined by a *b = min.{a, b}. Write the operation
table of the operation *.
15. Find the value of ‘a’ for which the function f defined as f(x) = {
𝑎 𝑠𝑖𝑛
𝜋
2
( 𝑥 + 1), 𝑥 ≤ 0
𝑡𝑎𝑛𝑥−𝑠𝑖𝑛𝑥
𝑥3
, 𝑥 > 0
is continuous at 0
16. Sand is pouring from a pipe at the rate of 12cm3
/s. The falling sand forms a cone on the ground in such
a way that the height of the cone is always one – sixth of the radius of the base. How is the height of the
sand cone increasing when the height is 4 cm?
17. Using elementary transformations, find the inverse of the matrix (
1 3 −2
−3 0 −1
2 1 0
) .
18. Evaluate : ∫ 2𝑠𝑖𝑛𝑥𝑐𝑜𝑠𝑥tan−1
( 𝑠𝑖𝑛 𝑥)
𝜋/2
0
𝑑𝑥dx.
19. If sin y = x sin(a + y), prove that
𝑑𝑦
𝑑𝑥
=
𝑠𝑖𝑛2
(𝑎+𝑦)
𝑠𝑖𝑛 𝑎
.
20. Evaluate : ∫
2
(1−𝑥)(1−𝑥2)
dx.
21. Find the point on the curve y = x3
– 11x + 5 at which the equation of tangent is y = x – 11.
22. Prove that : tan−1
(
cos 𝑥
1+sin𝑥
) =
𝜋
4
] −
𝑥
2
, 𝑥 ∈ (−
𝜋
2
,
𝜋
2
).
23. Using properties of determinants, prove that |
𝑏 + 𝑐 𝑞 + 𝑟 𝑦 + 𝑧
𝑐 + 𝑎 𝑟 + 𝑝 𝑧 + 𝑥
𝑎 + 𝑏 𝑝 + 𝑞 𝑥 + 𝑦
| = 2 |
𝑎 𝑝 𝑥
𝑏 𝑞 𝑦
𝑐 𝑟 𝑧
|
24. Let A = | 𝑅 − {3} 𝑎𝑛𝑑 𝐵 =| 𝑅 − {1}. Consider the function f : A → 𝐵 𝑑𝑒𝑓𝑖𝑛𝑒𝑑 𝑏𝑦 𝑓( 𝑥) = (
𝑥−2
𝑥−3
). Show
that f is one – one and onto and hence find f-1
.
25. Evaluate : ∫ (2𝑥2
+ 5𝑥
3
1
) dx as a limit of a sum.
2. 26. Prove that : 𝑡𝑎𝑛−1
(
1
12
) + tan−1
(
1
5
) + 𝑡𝑎𝑛−1
(
1
8
) + tan−1
(
1
7
) =
𝜋
4
27. If x = a sin t and y = a(cos t + log tan t/2), find
𝑑2 𝑦
𝑑𝑥2
.
28. Show that the function f(x) = | 𝑥 − 3|, 𝑥 ∈ | 𝑹 , is continuous but not differentiable at x = 3.
29. Evaluate : ∫
𝑠𝑖𝑛(𝑥−𝑎)
𝑠𝑖𝑛( 𝑥+𝑎)
dx.
30. Evaluate : ∫
𝑥2
(𝑥2+4)(𝑥2+9)
dx.
31. Using integration, find the area of the region enclosed between the two circles x2
+ y2
= 4 and (x – 2)2
+ y2
= 4.
32. Show that the differential equation 2ye x/y
dx + (y – 2x ex/y
) dy = 0 is homogeneous. Find the particular
Solution of this differential equation, given that x = 0 when y = 1.
33. Prove that 2 tan−1 (
1
5
) + sec−1(
5√2
7
) + 2 tan−1 (
1
8
) =
𝜋
4
34. Let A = {1, 2, 3,.......,9} and R be the relationinA A definedby(a,b) R (c,d) if a + d = b + c for(a, b),(c, d) inA A.
Prove that R isan equivalence relation.Alsoobtainthe equivalenceclass[(2,5)].
35. If y = xx
,prove that
𝑑2 𝑦
𝑑𝑥2
−
1
𝑦
(
𝑑𝑦
𝑑𝑥
)
2
−
𝑦
𝑥
= 0
36. Findthe area of the regioninthe firstquadrantenclosedbythe x- axis,the line y= x and the circle x2
+ y2
= 32.
37. Evaluate : ∫
𝑑𝑥
1+√ 𝑐𝑜𝑡𝑥
𝜋
3
𝜋
6
.
38. Evaluate: ∫
𝑑𝑥
𝑠𝑖𝑛𝑥−𝑠𝑖𝑛2𝑥
39. Verify Rolle’s Theorem for the function f(x) = x2
+ 2x – 8 x ∈ [-4, 2]
40. An open box with square base is to be made out of given quantity of cardboard of area c2
sq units. Show that the
maximum volume of the box is
𝑐3
6√3
cubic units.
41. Prove that volume of largest cone that can be inscribed in a sphere of radius ‘R’ is
8
27
of the volume of sphere. Also
find the height of cone.
42. If A = [
3 2 1
4 −1 2
7 3 −3
] find A-1
and by using A-1
solve : 3x+4y+7z=14, 2x-y+3z=4 , x+2y-3z=0
43. Find the particular solution of the differential equation : (x dy – y dx) y sin
𝑦
𝑥
= (y dx + x dy) x cos
𝑦
𝑥
, given that y =
𝜋, when x = 3.
44. Discuss the commutativity and associativity of the binary operation * on R defined by
a * b = a + b + ab, for all a,b ∈ R.
45. If (tan-1x)2 + (cot-1x)2 =
5𝜋2
8
, find x
46. If A = [
1 −1 0
2 3 4
0 1 2
] and B = [
2 2 −4
−4 2 −4
2 −1 5
] , find AB and solve the system x – y = 3, 2x + 3y + 4z = 17, y + 2z = 7.
47. Findthe equationof normal tothe curve x2
= 4y whichpassesthroughthe point(1,2)
48. The radiusof a spherical diamondismeasuredas7 cm withan error of 0.04cm . findthe approximate errorin
calculatingitsvolume.If the costof 1 c𝒎 𝟑 diamondisRs 1000, What isthe losstobuyerof the diamond?
49. Evaluate:∫
𝑥2
( 𝑥 𝑠𝑖𝑛 𝑥+𝑐𝑜𝑠 𝑥)2 dx