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 Continuity exercise 8.2 question 3 subquestion (vii) maths textbook solution

Please solve RD Sharma class 12 chapter Continuity exercise 8.2 question 3 subquestion (vii) maths textbook solution

Answers (1)

Answer:

 x = 0

Hint:

 Use L-Hospital Rule when we find 0/0 form

Given:

 f(x)=\left\{\begin{array}{cl} \frac{e^{x}-1}{\log _{e}(1-2 x)} & x \neq 0 \\ 7 & x=0 \end{array}\right.

Explanation:

At x = 0

\text { L.H.L } =\lim _{x \rightarrow 0^{-}} f(x)=\lim _{h \rightarrow 0}(0-h)=\lim _{h \rightarrow 0} \frac{e^{-h}-1}{\log _{e}(1-2 h)}

=\lim _{h \rightarrow 0} \frac{\frac{e^{-h}-1}{-h}}{\frac{\log _{e}(1-2 h)}{-2 h} \times 2}=\frac{1}{2}

\text { R.H.L }=\lim _{x \rightarrow 0^{+}} f(x)=\lim _{h \rightarrow 0}(0+h)=\lim _{h \rightarrow 0} \frac{e^{h}-1}{\log _{e}(1+2 h)}

=\lim _{h \rightarrow 0} \frac{\frac{e^{h}-1}{h}}{\frac{\log _{e}(2 h)}{2 h} \times 2}=\frac{1}{2}

\begin{aligned} &\text { Also } f(0)=7 \\ &\text { Thus L.H.L } =\text { R.H.L } \neq f(0) \end{aligned}

\thereforef(x) is not continuous at x = 0

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

CBSE launches entrance exam 2025, career guide for parents to plan for students' future
anam-khan

CBSE Class 12 Board Economics Paper Analysis: 'Student-friendly', well balanced with moderate difficulty
anam-khan

CBSE Class 12 Hindi exam 2025 not postponed; special exam for those who miss

Latest Question