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 8.1 Question 34 Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter 8 Continuity Exercise 8.1 Question 34 Maths Textbook Solution.

Answers (1)

best_answer

Answer:

                f\left ( 0 \right )=1

Hint:

f\left ( x \right ) must be defined. The limit of the f\left ( x \right ) approaches the value x must exist.

Given:

                f(x)=\frac{2 x+3 \sin x}{3 x+2 \sin x}, x \neq 0

Solution:

                \begin{aligned} &f(x)=\frac{2 x+3 \sin x}{3 x+2 \sin x}, x \neq 0 \\\\ &\lim _{x \rightarrow 0} f(x)=f(0)\\ \\ &\lim _{x \rightarrow 0} \frac{2 x+3 \sin x}{3 x+2 \sin x}=f(0) \\\\ &\lim _{x \rightarrow 0} \frac{x\left(2+3 \frac{\sin x}{x}\right)}{x\left(3+2 \frac{\sin x}{x}\right)}=f(0) \end{aligned} 

                \begin{aligned} &\lim _{x \rightarrow 0} \frac{\left(2+3 \frac{\sin x}{x}\right)}{\left(3+2 \frac{\sin x}{x}\right)}=f(0) \\\\ &\frac{\lim _{x \rightarrow 0}\left(2+3 \frac{\sin x}{x}\right)}{\lim _{x \rightarrow 0}\left(3+2 \frac{\sin x}{x}\right)}=f(0) \end{aligned}

                \frac{(2+3) \lim _{x \rightarrow 0}\left(\frac{\sin x}{x}\right)}{(3+2) \lim _{x \rightarrow 0}\left(\frac{\sin x}{x}\right)}=f(0)                                                                                       \left[\because \lim _{x \rightarrow 0} \frac{\sin x}{x}=1\right]

                \begin{aligned} &\frac{(2+3) 1}{(3+2) 1}=f(0) \\ &\frac{5}{5}=f(0) \\ &f(0)=1 \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

CBSE asks schools to ensure error-free LOC forms for Classes 10, 12; edit window from October 13
anam-khan

‘You ruined my career’: Students hit back at CBSE over 'abrupt' removal of additional subjects
anam-khan

‘Careers are at stake’: CBSE removes additional subject option for private students without prior notice

Latest Question