Question

For the function $\begin{cases}\ \textless \ br /\ \textgreater \ \frac{e^{1/x} -1}{e^{1/x}+1} & x \neq 0 \\ \ \textless \ br /\ \textgreater \ 0 & x = 0\ \textless \ br /\ \textgreater \ \end{cases}$ which of the following is correct?

(a) $\large\rm { \displaystyle\lim_{\rm{ x \to 0} f(x)}}$ doesn't exist $\large\rm { \nexists}$

(b) $\large\rm { \displaystyle\lim_{\rm{ x \to 0} f(x)} = 1}$

(c) $\large\rm { \displaystyle\lim_{\rm{ x \to 0} f(x)}}$ exist $\large\rm { \exists}$ but f(x) is not continuous at x=0.

(d) f(x) is continuous at x=0.
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Answer 1

Refer to the Attachment !!!!