Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Please solve RD Sharma class 12 chapter 8 Continuity exercise Fill in the blanks question 13 maths textbook solution

Please solve RD Sharma class 12 chapter 8 Continuity exercise Fill in the blanks question 13 maths textbook solution

Answers (1)

Answer: \pi

Hint: Use the identity \frac{\sin x}{x}=1

Given:

           f(x)=x\sin \left ( \frac{\pi }{x} \right )  is continuous everywhere

Solution:

             f(x)=x\sin \left ( \frac{\pi }{3} \right )  is continuous

            \begin{aligned} &\lim _{x \rightarrow 0} f(x)=f(0) \\ &\lim _{x \rightarrow 0} x \sin \left(\frac{\pi}{x}\right)=f(0) \\ &\lim _{x \rightarrow 0} \frac{x \sin \left(\frac{\pi}{x}\right)}{\frac{\pi}{x}} \times \frac{\pi}{x}=f(0) \end{aligned}

            \begin{aligned} &\lim _{x \rightarrow 0} x \times \frac{\pi}{x}=f(0) \\ &\lim _{x \rightarrow 0} \pi=f(0) \\ &f(0)=\pi \; \; \; \; \; \; \; \; \; \; \; \quad\left[\because \lim _{x \rightarrow 0} \frac{\sin x}{x}=1\right] \end{aligned}\begin{aligned} &\lim _{x \rightarrow 0} x \times \frac{\pi}{x}=f(0) \\ &\lim _{x \rightarrow 0} \pi=f(0) \\ &f(0)=\pi \; \; \; \; \; \; \; \; \; \; \; \quad\left[\because \lim _{x \rightarrow 0} \frac{\sin x}{x}=1\right] \end{aligned}\begin{aligned} &\lim _{x \rightarrow 0} x \times \frac{\pi}{x}=f(0) \\ &\lim _{x \rightarrow 0} \pi=f(0) \\ &f(0)=\pi \; \; \; \; \; \; \; \; \; \; \; \quad\left[\because \lim _{x \rightarrow 0} \frac{\sin x}{x}=1\right] \end{aligned}

Posted by

infoexpert26

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

'Award grace marks': CBSE's July 28 supplementary exam sparks student outrage over college admissions
anam-khan

CBSE Class 12 supplementary exam 2026 on July 28; LOC submission starts
anam-khan

CBSE OSM Evaluation Row: Class 12 revised marksheet sparks fresh debate, Vedant disputes board's explanation

Latest Question