Civil Engineering (CE) Exam > Civil Engineering (CE) Videos > Engineering Mathematics > Calculus: Mean Value Theorem (Rolles, Lagrange & Cauchy)
Calculus: Mean Value Theorem (Rolles, Lagrange & Cauchy) Video Lecture | Engineering Mathematics - Civil Engineering (CE)
|
65 videos|120 docs|94 tests
|
FAQs on Calculus: Mean Value Theorem (Rolles, Lagrange & Cauchy) Video Lecture - Engineering Mathematics - Civil Engineering (CE)
| 1. What is the Mean Value Theorem in calculus? |  |
Ans. The Mean Value Theorem states that if a function is continuous on a closed interval [a, b] and differentiable on the open interval (a, b), then there exists at least one point c in (a, b) where the derivative of the function is equal to the average rate of change of the function over [a, b].
| 2. What is the significance of the Mean Value Theorem in calculus? | |
Ans. The Mean Value Theorem is significant in calculus as it provides a fundamental result that guarantees the existence of a point where the instantaneous rate of change of a function equals its average rate of change over a given interval. It serves as a cornerstone for many other theorems and techniques in calculus.
| 3. How is the Mean Value Theorem related to Rolle's Theorem? | |
Ans. The Mean Value Theorem is an extension of Rolle's Theorem. Rolle's Theorem states that if a function is continuous on a closed interval [a, b], differentiable on the open interval (a, b), and the function values at the endpoints are equal, then there exists at least one point c in (a, b) where the derivative of the function is zero. The Mean Value Theorem is a generalized version of Rolle's Theorem, where the condition of equal function values at the endpoints is relaxed.
| 4. How is the Mean Value Theorem related to Lagrange's Mean Value Theorem? | |
Ans. Lagrange's Mean Value Theorem is a specific case of the Mean Value Theorem. It states that if a function is continuous on a closed interval [a, b] and differentiable on the open interval (a, b), then there exists at least one point c in (a, b) where the derivative of the function is equal to the slope of the secant line connecting the endpoints of the interval. The Mean Value Theorem is a more general statement that encompasses Lagrange's Mean Value Theorem.
| 5. What is Cauchy's Mean Value Theorem in calculus? | |
Ans. Cauchy's Mean Value Theorem is a variation of the Mean Value Theorem that applies to the ratio of two functions. It states that if two functions, f(x) and g(x), are continuous on a closed interval [a, b] and differentiable on the open interval (a, b), and g(x) ≠ 0 for all x in (a, b), then there exists at least one point c in (a, b) where the derivative of f(x) divided by the derivative of g(x) is equal to the ratio of their values at c. Cauchy's Mean Value Theorem provides a way to relate the derivatives of two functions.
Related Exams
About this Video
|
4.71/5 Rating |
|
Nov 21, 2024 Last updated |
Video Description: Calculus: Mean Value Theorem (Rolles, Lagrange & Cauchy) for Civil Engineering (CE) 2024 is part of Engineering Mathematics preparation.
The notes and questions for Calculus: Mean Value Theorem (Rolles, Lagrange & Cauchy) have been prepared according to the Civil Engineering (CE) exam syllabus.
Information about Calculus: Mean Value Theorem (Rolles, Lagrange & Cauchy) covers all important topics for Civil Engineering (CE) 2024 Exam.
Find important definitions, questions, notes, meanings, examples, exercises and tests below for Calculus: Mean Value Theorem (Rolles, Lagrange & Cauchy).
Introduction of Calculus: Mean Value Theorem (Rolles, Lagrange & Cauchy) in English is available as part of our Engineering Mathematics for Civil Engineering (CE) & Calculus: Mean Value Theorem (Rolles, Lagrange & Cauchy) in
Hindi for Engineering Mathematics course. Download more important topics related with notes, lectures and mock test series for
Civil Engineering (CE) Exam by signing up for free.
Description
Video Lecture & Questions for Calculus: Mean Value Theorem (Rolles, Lagrange & Cauchy) Video Lecture | Engineering Mathematics - Civil Engineering (CE) - Civil Engineering (CE) full syllabus preparation | Free video for Civil Engineering (CE) exam to prepare for Engineering Mathematics.
Information about Calculus: Mean Value Theorem (Rolles, Lagrange & Cauchy)
Here you can find the meaning of Calculus: Mean Value Theorem (Rolles, Lagrange & Cauchy) defined & explained in the simplest way possible.
Besides explaining types of Calculus: Mean Value Theorem (Rolles, Lagrange & Cauchy) theory, EduRev gives you an ample number of questions to practice Calculus: Mean Value Theorem (Rolles, Lagrange & Cauchy) tests,
examples and also practice Civil Engineering (CE) tests.
|
65 videos|120 docs|94 tests
|
|
Explore Courses for Civil Engineering (CE) exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
Related Searches
mock tests for examination
,Exam
,Sample Paper
,Calculus: Mean Value Theorem (Rolles
,ppt
,video lectures
,Important questions
,Lagrange & Cauchy) Video Lecture | Engineering Mathematics - Civil Engineering (CE)
,past year papers
,shortcuts and tricks
,MCQs
,Extra Questions
,Summary
,Previous Year Questions with Solutions
,Lagrange & Cauchy) Video Lecture | Engineering Mathematics - Civil Engineering (CE)
,practice quizzes
,Objective type Questions
,Semester Notes
,Free
,Calculus: Mean Value Theorem (Rolles
,study material
,Calculus: Mean Value Theorem (Rolles
,Lagrange & Cauchy) Video Lecture | Engineering Mathematics - Civil Engineering (CE)
,Viva Questions
;
Study Calculus: Mean Value Theorem (Rolles, Lagrange & Cauchy) on the App
Students of Civil Engineering (CE) can study Calculus: Mean Value Theorem (Rolles, Lagrange & Cauchy) alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the Calculus: Mean Value Theorem (Rolles, Lagrange & Cauchy),
students can also utilize the EduRev App for other study materials such as previous year question papers, syllabus, important questions, etc.
The EduRev App will make your learning easier as you can access it from anywhere you want.
The content of Calculus: Mean Value Theorem (Rolles, Lagrange & Cauchy) is prepared as per the latest Civil Engineering (CE) syllabus.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup