1) The document discusses hyperbolic functions including their definitions, derivatives, inverses, and identities. It provides examples of calculating derivatives of hyperbolic functions using the chain rule.
2) Applications of hyperbolic functions include modeling the shape of a cable suspended between two points and the velocity of ocean waves.
3) The inverse hyperbolic functions can be expressed in terms of logarithms, such as sinh-1x = ln(x + √(x2 + 1)).
On Application of Power Series Solution of Bessel Problems to the Problems of...BRNSS Publication Hub
One of the most powerful techniques available for studying functions defined by differential equations is to produce power series expansions of their solutions when such expansions exist. This is the technique I now investigated, in particular, its feasibility in the solution of an engineering problem known as the problem of strut of variable moment of inertia. In this work, I explored the basic theory of the Bessel’s function and its power series solution. Then, a model of the problem of strut of variable moment of inertia was developed into a differential equation of the Bessel’s form, and finally, the Bessel’s equation so formed was solved and result obtained.
On Application of Power Series Solution of Bessel Problems to the Problems of...BRNSS Publication Hub
One of the most powerful techniques available for studying functions defined by differential equations is to produce power series expansions of their solutions when such expansions exist. This is the technique I now investigated, in particular, its feasibility in the solution of an engineering problem known as the problem of strut of variable moment of inertia. In this work, I explored the basic theory of the Bessel’s function and its power series solution. Then, a model of the problem of strut of variable moment of inertia was developed into a differential equation of the Bessel’s form, and finally, the Bessel’s equation so formed was solved and result obtained.
I am Frank P. I am a Physical Chemistry Assignment Expert at eduassignmenthelp.com. I hold a Ph.D. in Physical Chemistry, from Malacca, Malaysia. I have been helping students with their homework for the past 6 years. I solve assignments related to Physical Chemistry.
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Solution manual for introduction to nonlinear finite element analysis nam-h...Salehkhanovic
Solution Manual for Introduction to Nonlinear Finite Element Analysis
Author(s) : Nam-Ho Kim
This solution manual include all problems (Chapters 1 to 5) of textbook. There is one PDF for each of chapters.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
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I am Frank P. I am a Physical Chemistry Assignment Expert at eduassignmenthelp.com. I hold a Ph.D. in Physical Chemistry, from Malacca, Malaysia. I have been helping students with their homework for the past 6 years. I solve assignments related to Physical Chemistry.
Visit eduassignmenthelp.com or email info@eduassignmenthelp.com.
You can also call on +1 678 648 4277 for any assistance with Physical Chemistry Assignments.
Solution manual for introduction to nonlinear finite element analysis nam-h...Salehkhanovic
Solution Manual for Introduction to Nonlinear Finite Element Analysis
Author(s) : Nam-Ho Kim
This solution manual include all problems (Chapters 1 to 5) of textbook. There is one PDF for each of chapters.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
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.
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
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
Safalta Digital marketing institute in Noida, provide complete applications that encompass a huge range of virtual advertising and marketing additives, which includes search engine optimization, virtual communication advertising, pay-per-click on marketing, content material advertising, internet analytics, and greater. These university courses are designed for students who possess a comprehensive understanding of virtual marketing strategies and attributes.Safalta Digital Marketing Institute in Noida is a first choice for young individuals or students who are looking to start their careers in the field of digital advertising. The institute gives specialized courses designed and certification.
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42. Derivative of Parametric Equations
Consider the graph of
x = 2 sin t, y = cos t
We seek the slope, that
is
𝑑𝑦
𝑑𝑥
=
𝑑𝑦
𝑑𝑡
.
𝑑𝑡
𝑑𝑥
For parametric equations:
𝑑𝑦
𝑑𝑥
=
𝑑𝑦/𝑑𝑡
𝑑𝑥/𝑑𝑡
For our example :
𝑑𝑦
𝑑𝑥
=
− sin 𝑡
2 cos 𝑡
=
− tan 𝑡
2
43. Second Derivatives
The second derivative is the derivative of the
first derivative
But the first derivative is a function of t
We seek the derivative with respect to x
We must use the chain rule
𝑑2𝑦
𝑑𝑥2 =
𝑑
𝑑𝑥
𝑦′
=
𝑑
𝑑𝑡
𝑦′
.
𝑑𝑡
𝑑𝑥
=
𝑑
𝑑𝑡
𝑦′
𝑑𝑥
𝑑𝑡
44. Second Derivatives
Find the second derivative of the parametric
equations
x = 3 + 4cos t
y = 1 – sin t
First derivative:
𝑑𝑦
𝑑𝑥
=
𝑦.
𝑥. =
− 𝑐𝑜𝑠 𝑡
−4 sin 𝑡
=
cot 𝑡
4
Second derivative:
𝑑2𝑦
𝑑𝑥2 =
𝑑
𝑑𝑡
𝑦′
.
𝑑𝑡
𝑑𝑥
=
−1
4
csc2𝑡
−4 sin 𝑡
∴ 𝑦′′
=
1
16 sin3𝑡
45. Try This!
Where does the curve described by the
parametric equations have a horizontal tangent?
x = t – 4
y = (t 2 + t)2
Find the derivative
For what value of t does dy/dx = 0?