For the function f(x) , = _e (1 + x) - _e (1 - x) x to be continu… - Vidyadip

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

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Answer

d
(d) By $L-$ Hospital’s rule $\mathop {\lim }\limits_{x \to 0} f(x)$ is $2$.

Therefore, for $f(x)$ to be continuous, the value of function should be $2$.

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