Functions Question 428

Question: For the function $ f(x),=\frac{{\log_{e}}(1+x)-{\log_{e}}(1-x)}{x} $ to be continuous at $ x=0, $ the value of $ f(0), $ should be

[MP PET 2003]

Options:

A) ?1

B) 0

C) ?2

D) 2

Show Answer

Answer:

Correct Answer: D

Solution:

By L-Hospital?s rule $ \underset{x\to 0}{\mathop{\lim }},f(x) $ is 2. Therefore, for $ f(x) $ to be continuous, the value of function should be 2.