Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Need solution for RD Sharma maths class 12 chapter 8 Continuity exercise multiple choice question 35

Need solution for RD Sharma maths class 12 chapter 8 Continuity exercise multiple choice question 35

Answers (1)

Answer:

 The correct option is (a)

Hint:

 (i) A function f(x) is said to be continuous at a point x = a of its domain, if

\begin{aligned} &\lim _{x \rightarrow a} f(x)=f(a) \\ &\lim _{x \rightarrow a^{+}} f(a+h)=\lim _{x \rightarrow a^{-}} f(a-h)=f(a) \end{aligned}

(ii) Standard limits

\begin{aligned} &\lim _{x \rightarrow 0} \frac{\sin x}{x}=1 \\ &\text { (iii) } \lim _{x \rightarrow 0}\{f(x) \pm g(x)\}=1 \pm m \text {, } \end{aligned}

\begin{aligned} &{\text { Where, }} \lim _{x \rightarrow a} f(x)=1, \lim _{x \rightarrow a} g(x)=m \\ \end{aligned}

Given:

 \begin{aligned} & f(x)=x \sin \frac{1}{x} \end{aligned}

Solution:

\begin{aligned} & f(x)=x \sin \frac{1}{x} \end{aligned}

=\lim _{x \rightarrow 0} f(x)=\lim _{x \rightarrow 0} x \sin \frac{1}{x}=0

Function f(x) is continuous at x = 0

\begin{aligned} &=\lim _{x \rightarrow 0} f(x)=f(0) \\ &=0=f(0) \end{aligned}

So, option (a) is correct.

Posted by

Gurleen Kaur

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