Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Explain solution RD Sharma class 12 Chapter 8 Continuity exercise 8.1 question 20

Explain solution RD Sharma class 12 Chapter 8 Continuity exercise 8.1 question 20

Answers (1)

Answer:

                k=\frac{5}{3}

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)=\left\{\begin{array}{c} \frac{\sin 5 x}{3 x}, \text { if } x \neq 0 \\\\ k, \text { if } x=0 \end{array}\right.    is continuous at  x=0

Solution:

                f(x)=\left(\begin{array}{c} \frac{\sin 5 x}{3 x}, \text { if } x \neq 0 \\\\ k, \text { if } x=0 \end{array}\right)

If  f\left ( x \right ) is continuous at x=0 , then

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

                \lim _{x \rightarrow 0} \frac{5 \sin 5 x}{3 \times 5 x}=k   [Multiplying and dividing by 5 ]

                \frac{5}{3} \lim _{x \rightarrow 0} \frac{\sin 5 x}{5 x}=k                                                                           \left[\because \lim _{x \rightarrow 0} \frac{\sin x}{x}=1\right]

                \begin{aligned} &\frac{5}{3} \times 1=k \\ &k=\frac{5}{3} \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

PM Modi's Pariksha Pe Charcha 2025 to be held next month, registrations open till January 14
anam-khan

CBSE Board Exams 2025: Online portal for availing exemptions by CWSN students opens
anam-khan

Board Exams: States agree to equivalence; no question paper ‘jumbling’ from next year, says PARAKH CEO

Latest Question