Limits Continuity And Differentiability Question 112
Question: The function $ f(x)=\frac{{{(3^{x}-1)}^{2}}}{\sin x\cdot \ln (1+x)},x\ne 0 $ , is continuous at x=0. Then the value of f(0) is
Options:
A) $ 2{\log _{e}}3 $
B) $ {{(2{\log _{e}}3)}^{2}} $
C) $ {\log _{e}}6 $
D) none of these
Show Answer
Answer:
Correct Answer: B
Solution:
Given f(x) is continuous at x=0.
Therefore, $ \underset{x\to 0}{\mathop{\lim }}f(x)=f(0) $
Or $ \underset{x\to 0}{\mathop{\lim }}\frac{{{(3^{x}-1)}^{2}}}{\sin x\ln (1+x)}=f(0) $
Or $ f(0)=\underset{x\to 0}{\mathop{\lim }}\frac{{{( \frac{3^{x}-1}{x} )}^{2}}}{( \frac{\sin x}{x} )( \frac{\ln (1+x)}{x} )}={{(ln3)}^{2}} $
BETA
