Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Provide Solutio for RD Sharma Class 12 Chapter Continuity Exercise 8.1 Question 36 Subquestion (iv)

Provide Solutio for RD Sharma Class 12 Chapter Continuity Exercise 8.1 Question 36 Subquestion (iv)

Answers (1)

Answer:

                k=\frac{-2}{\pi}

Hint:

 For a function to be continuous at a point, its LHL RHL and value at that point should be equal.

 

Given:

                f(x)=\left\{\begin{array}{l} k x+1, \text { if } x \leq \pi \\\\ \cos x, \text { if } x>\pi \end{array}\right.

               

Solution:

                f(x)=\left\{\begin{array}{l} k x+1, \text { if } x \leq \pi \\\\ \cos x, \text { if } x>\pi \end{array}\right.

We have

(LHL at x=\pi )

                \lim _{x \rightarrow \pi^{-}} f(x)=\lim _{h \rightarrow 0} f(\pi-h)=\lim _{h \rightarrow 0} k(\pi-h)+1=k \pi+1

(RHL at x=\pi )

                \lim _{x \rightarrow \pi^{+}} f(x)=\lim _{h \rightarrow 0} f(\pi+h)=\lim _{h \rightarrow 0} \cos (\pi+h)=\cos \pi=-1

If f\left ( x \right ) is continuous at x=\pi , then

                \begin{aligned} &\lim _{x \rightarrow \pi^{+}} f(x)=\lim _{x \rightarrow \pi^{-}} f(x) \\ &k \pi+1=-1 \\ &k=\frac{-2}{\pi} \end{aligned}

               

 

Posted by

infoexpert27

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

Board Exam Time Table 2025 Live: UP Board exams from February 24; CBSE, BSEB date sheet soon
anam-khan

CBSE Date Sheet 2025 Live: Class 10, 12 board exam dates soon; syllabus, sample papers
anam-khan

Extra time in CBSE exams for students with type 1 diabetes: Kerala SHRC seeks report on plea

Latest Question