Question

If \(f(x)=\begin{cases} xe^{-(\frac{1}{|x|}+\frac{1}{x})}; & \text{if } x\ne0 \text{ then} \\ 0\ \ \ \ \ \ \ \ \ \ \ \ \ \ ; & \text{if }x=0\end{cases}\)
which of the following is correct ?

• A. f(x) is continuous and f'(0) does not exist
• B. f(x) is not continuous
• C. f(x) is continuous and f'(0) also exists
• D. None of these

Answer 1

The Correct Option is A

The correct option is (A) : f(x) is continuous and f'(0) does not exist.