JEE Exam > JEE Notes > Mathematics (Maths) Class 12 > RD Sharma Class 12 Solutions - Differentiability
RD Sharma Class 12 Solutions - Differentiability | Mathematics (Maths) Class 12 - JEE PDF Download
| Download, print and study this document offline |
Please wait while the PDF view is loading
Page 1 10. Differentiability Exercise 10.1 1. Question Show that f(x) = |x - 3| is continuous but not differentiable at x = 3. Answer f(x) = |x – 3| Therefore we can write it as, f(3) = 3 - 3 = 0 LHL = = = = RHL = = = = 0 LHL = RHL = f(3) Since, f(x) is continuous at x = 3 (LHD at x = 3) = = = = = - 1 (RHD at x = 3) = = = = = 1 (LHD at x = 3) (RHD at x = 3) Page 2 10. Differentiability Exercise 10.1 1. Question Show that f(x) = |x - 3| is continuous but not differentiable at x = 3. Answer f(x) = |x – 3| Therefore we can write it as, f(3) = 3 - 3 = 0 LHL = = = = RHL = = = = 0 LHL = RHL = f(3) Since, f(x) is continuous at x = 3 (LHD at x = 3) = = = = = - 1 (RHD at x = 3) = = = = = 1 (LHD at x = 3) (RHD at x = 3) Hence, f(x) is continuous but not differentiable at x = 3. 2. Question Show that f(x) = is not differentiable at x = 0. Answer For differentiability, LHD(at x = 0) = RHD (at x = 0) (LHD at x = 0) = = = = = = = Not defined (RHD at x = 3) = = = = = = Not defined Since, LHD and RHD does not exist at x = 0 Hence, f(x) is not differentiable at x = 0 3. Question Show that is differentiable at x = 3. Also, find f’(3). Answer For differentiability, LHD(at x = 3) = RHD (at x = 3) (LHD at x = 3) = Page 3 10. Differentiability Exercise 10.1 1. Question Show that f(x) = |x - 3| is continuous but not differentiable at x = 3. Answer f(x) = |x – 3| Therefore we can write it as, f(3) = 3 - 3 = 0 LHL = = = = RHL = = = = 0 LHL = RHL = f(3) Since, f(x) is continuous at x = 3 (LHD at x = 3) = = = = = - 1 (RHD at x = 3) = = = = = 1 (LHD at x = 3) (RHD at x = 3) Hence, f(x) is continuous but not differentiable at x = 3. 2. Question Show that f(x) = is not differentiable at x = 0. Answer For differentiability, LHD(at x = 0) = RHD (at x = 0) (LHD at x = 0) = = = = = = = Not defined (RHD at x = 3) = = = = = = Not defined Since, LHD and RHD does not exist at x = 0 Hence, f(x) is not differentiable at x = 0 3. Question Show that is differentiable at x = 3. Also, find f’(3). Answer For differentiability, LHD(at x = 3) = RHD (at x = 3) (LHD at x = 3) = = = = = = 12 (RHD at x = 3) = = = = = = = 12 Since, (LHD at x = 3) = (RHD at x = 3) Hence, f(x) is differentiable at x = 3. 4. Question Show that the function f defined as follows, Is continuous at x = 2, but not differentiable there at x = 2. Answer For continuity, LHl(at x = 2) = RHL (at x = 2) f(2) = 2(2) 2 - 2 = 8 - 2 = 6 LHL = = = = 8 - 2 = 6 RHL = Page 4 10. Differentiability Exercise 10.1 1. Question Show that f(x) = |x - 3| is continuous but not differentiable at x = 3. Answer f(x) = |x – 3| Therefore we can write it as, f(3) = 3 - 3 = 0 LHL = = = = RHL = = = = 0 LHL = RHL = f(3) Since, f(x) is continuous at x = 3 (LHD at x = 3) = = = = = - 1 (RHD at x = 3) = = = = = 1 (LHD at x = 3) (RHD at x = 3) Hence, f(x) is continuous but not differentiable at x = 3. 2. Question Show that f(x) = is not differentiable at x = 0. Answer For differentiability, LHD(at x = 0) = RHD (at x = 0) (LHD at x = 0) = = = = = = = Not defined (RHD at x = 3) = = = = = = Not defined Since, LHD and RHD does not exist at x = 0 Hence, f(x) is not differentiable at x = 0 3. Question Show that is differentiable at x = 3. Also, find f’(3). Answer For differentiability, LHD(at x = 3) = RHD (at x = 3) (LHD at x = 3) = = = = = = 12 (RHD at x = 3) = = = = = = = 12 Since, (LHD at x = 3) = (RHD at x = 3) Hence, f(x) is differentiable at x = 3. 4. Question Show that the function f defined as follows, Is continuous at x = 2, but not differentiable there at x = 2. Answer For continuity, LHl(at x = 2) = RHL (at x = 2) f(2) = 2(2) 2 - 2 = 8 - 2 = 6 LHL = = = = 8 - 2 = 6 RHL = = = = 6 Since, LHL = RHL = f(2) Hence, F(x) is continuous at x = 2 For differentiability, LHD(at x = 2) = RHD (at x = 2) (LHD at x = 2) = = = = = = = = 6 (RHD at x = 2) = = = = = 5 Since, (RHD at x = 2) (LHD at x = 2) Hence, f(2) is not differentiable at x = 2. 5. Question Discuss the continuity and differentiability of f(x) = |x| + |x - 1| in the interval ( - 1,2). Answer f(x) = f(x) = We know that a polynomial and a constant function is continuous and differentiable every where. So, f(x) is continuous and differentiable for x ( - 1,0) and x (0,1) and (1,2). Page 5 10. Differentiability Exercise 10.1 1. Question Show that f(x) = |x - 3| is continuous but not differentiable at x = 3. Answer f(x) = |x – 3| Therefore we can write it as, f(3) = 3 - 3 = 0 LHL = = = = RHL = = = = 0 LHL = RHL = f(3) Since, f(x) is continuous at x = 3 (LHD at x = 3) = = = = = - 1 (RHD at x = 3) = = = = = 1 (LHD at x = 3) (RHD at x = 3) Hence, f(x) is continuous but not differentiable at x = 3. 2. Question Show that f(x) = is not differentiable at x = 0. Answer For differentiability, LHD(at x = 0) = RHD (at x = 0) (LHD at x = 0) = = = = = = = Not defined (RHD at x = 3) = = = = = = Not defined Since, LHD and RHD does not exist at x = 0 Hence, f(x) is not differentiable at x = 0 3. Question Show that is differentiable at x = 3. Also, find f’(3). Answer For differentiability, LHD(at x = 3) = RHD (at x = 3) (LHD at x = 3) = = = = = = 12 (RHD at x = 3) = = = = = = = 12 Since, (LHD at x = 3) = (RHD at x = 3) Hence, f(x) is differentiable at x = 3. 4. Question Show that the function f defined as follows, Is continuous at x = 2, but not differentiable there at x = 2. Answer For continuity, LHl(at x = 2) = RHL (at x = 2) f(2) = 2(2) 2 - 2 = 8 - 2 = 6 LHL = = = = 8 - 2 = 6 RHL = = = = 6 Since, LHL = RHL = f(2) Hence, F(x) is continuous at x = 2 For differentiability, LHD(at x = 2) = RHD (at x = 2) (LHD at x = 2) = = = = = = = = 6 (RHD at x = 2) = = = = = 5 Since, (RHD at x = 2) (LHD at x = 2) Hence, f(2) is not differentiable at x = 2. 5. Question Discuss the continuity and differentiability of f(x) = |x| + |x - 1| in the interval ( - 1,2). Answer f(x) = f(x) = We know that a polynomial and a constant function is continuous and differentiable every where. So, f(x) is continuous and differentiable for x ( - 1,0) and x (0,1) and (1,2). We need to check continuity and differentiability at x = 0 and x = 1. Continuity at x = 0 = 1 = 1 F(0) = 1 Since, f(x) is continuous at x = 0 Continuity at x = 1 = 1 = 1 F(1) = 1 = 1 Since, f(x) is continuous at x = 1 For differentiability, LHD(at x = 0) = RHD (at x = 0) Differentiability at x = 0 (LHD at x = 0) = = = = 2 (RHD at x = 0) = = = = 0 Since,(LHD at x = 0) (RHD at x = 0) So, f(x) is differentiable at x = 0. For differentiability, LHD(at x = 1) = RHD (at x = 1) Differentiability at x = 1 (LHD at x = 1) = = = 0Read More
|
204 videos|290 docs|139 tests
|
About this Document
|
4.89/5 Rating |
|
Dec 25, 2024 Last updated |
Document Description: RD Sharma Class 12 Solutions - Differentiability for JEE 2024 is part of Mathematics (Maths) Class 12 preparation.
The notes and questions for RD Sharma Class 12 Solutions - Differentiability have been prepared according to the JEE exam syllabus. Information about RD Sharma Class 12 Solutions - Differentiability covers topics
like and RD Sharma Class 12 Solutions - Differentiability Example, for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for RD Sharma Class 12 Solutions - Differentiability.
Introduction of RD Sharma Class 12 Solutions - Differentiability in English is available as part of our Mathematics (Maths) Class 12
for JEE & RD Sharma Class 12 Solutions - Differentiability in Hindi for Mathematics (Maths) Class 12 course.
Download more important topics related with notes, lectures and mock test series for JEE
Exam by signing up for free. JEE: RD Sharma Class 12 Solutions - Differentiability | Mathematics (Maths) Class 12 - JEE
Description
Full syllabus notes, lecture & questions for RD Sharma Class 12 Solutions - Differentiability | Mathematics (Maths) Class 12 - JEE - JEE | Plus excerises question with solution to help you revise complete syllabus for Mathematics (Maths) Class 12 | Best notes, free PDF download
Information about RD Sharma Class 12 Solutions - Differentiability
In this doc you can find the meaning of RD Sharma Class 12 Solutions - Differentiability defined & explained in the simplest way possible. Besides explaining types of
RD Sharma Class 12 Solutions - Differentiability theory, EduRev gives you an ample number of questions to practice RD Sharma Class 12 Solutions - Differentiability tests, examples and also practice JEE
tests
|
Explore Courses for JEE exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
Related Searches
RD Sharma Class 12 Solutions - Differentiability | Mathematics (Maths) Class 12 - JEE
,Important questions
,study material
,Exam
,MCQs
,Semester Notes
,Summary
,RD Sharma Class 12 Solutions - Differentiability | Mathematics (Maths) Class 12 - JEE
,practice quizzes
,video lectures
,RD Sharma Class 12 Solutions - Differentiability | Mathematics (Maths) Class 12 - JEE
,Extra Questions
,Viva Questions
,Previous Year Questions with Solutions
,shortcuts and tricks
,Sample Paper
,mock tests for examination
,past year papers
,Objective type Questions
,Free
,ppt
;
Additional Information about RD Sharma Class 12 Solutions - Differentiability for JEE Preparation
RD Sharma Class 12 Solutions - Differentiability Free PDF Download
The RD Sharma Class 12 Solutions - Differentiability is an invaluable resource that delves deep into the core of the JEE exam.
These study notes are curated by experts and cover all the essential topics and concepts, making your preparation more efficient and effective.
With the help of these notes, you can grasp complex subjects quickly, revise important points easily,
and reinforce your understanding of key concepts. The study notes are presented in a concise and easy-to-understand manner,
allowing you to optimize your learning process. Whether you're looking for best-recommended books, sample papers, study material,
or toppers' notes, this PDF has got you covered. Download the RD Sharma Class 12 Solutions - Differentiability now and kickstart your journey towards success in the JEE exam.
Importance of RD Sharma Class 12 Solutions - Differentiability
The importance of RD Sharma Class 12 Solutions - Differentiability cannot be overstated, especially for JEE aspirants.
This document holds the key to success in the JEE exam.
It offers a detailed understanding of the concept, providing invaluable insights into the topic.
By knowing the concepts well in advance, students can plan their preparation effectively.
Utilize this indispensable guide for a well-rounded preparation and achieve your desired results.
RD Sharma Class 12 Solutions - Differentiability Notes
RD Sharma Class 12 Solutions - Differentiability Notes offer in-depth insights into the specific topic to help you master it with ease.
This comprehensive document covers all aspects related to RD Sharma Class 12 Solutions - Differentiability.
It includes detailed information about the exam syllabus, recommended books, and study materials for a well-rounded preparation.
Practice papers and question papers enable you to assess your progress effectively.
Additionally, the paper analysis provides valuable tips for tackling the exam strategically.
Access to Toppers' notes gives you an edge in understanding complex concepts.
Whether you're a beginner or aiming for advanced proficiency, RD Sharma Class 12 Solutions - Differentiability Notes on EduRev are your ultimate resource for success.
RD Sharma Class 12 Solutions - Differentiability JEE Questions
The "RD Sharma Class 12 Solutions - Differentiability JEE Questions" guide is a valuable resource for all aspiring students preparing for the
JEE exam. It focuses on providing a wide range of practice questions to help students gauge
their understanding of the exam topics. These questions cover the entire syllabus, ensuring comprehensive preparation.
The guide includes previous years' question papers for students to familiarize themselves with the exam's format and difficulty level.
Additionally, it offers subject-specific question banks, allowing students to focus on weak areas and improve their performance.
Study RD Sharma Class 12 Solutions - Differentiability on the App
Students of JEE can study RD Sharma Class 12 Solutions - Differentiability alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the RD Sharma Class 12 Solutions - Differentiability,
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 RD Sharma Class 12 Solutions - Differentiability is prepared as per the latest JEE syllabus.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup