The function f(z) defined by (f(z)= \begin{cases} \frac{... | Mathematics | SolveeIt | Solveeit

Today, August 23

Question

The function f(z) defined by $f(z)= \begin{cases} \frac{Re(z)}{z} & z\neq0\\\ 0 & z=0 \end{cases}$ then which one of the following is true?

A

$\lim\limits_{z\rightarrow0}f(z)$ exists

B

f(z) is continuous at z=0

C

f(z) is differentiable everywhere

D

f(z) is not continuous at z=0

Answer

f(z) is not continuous at z=0

Explanation

Solution

The correct answer is(D): f(z) is not continuous at z=0