Which one of the following is not true always ?

Question

Which one of the following is not true always ? (A) If a function f(x) is continuous at x = a , then limx → a f(x) exists (B) If f(x) and g(x) are differentiable at x = a, then f(x) + g(x) is also differentiable at x = a (C) If f (x) is continuous at x = a, then it is differentiable at x = a (D) If f(x) is not continuous at x = a, then it is not differentiable at x = a

Tardigrade Admin · Accepted Answer

If a function f(x) is continuous at x=a, then it may or may not be differentiable at x=a

Q. Which one of the following is not true always ?

If a function $f (x)$ is continuous at $x = a$ , then $lim_{x \to a} f (x)$ exists

If $f (x)$ and $g (x)$ are differentiable at $x = a$ , then $f (x) + g (x)$ is also differentiable at $x = a$

If $f (x)$ is continuous at $x = a$ , then it is differentiable at $x = a$

If $f (x)$ is not continuous at $x = a$ , then it is not differentiable at $x = a$

If a function $f (x)$ is continuous at $x = a$ , then it may or may not be differentiable at $x = a$

Q. Which one of the following is not true always ?

If a function f(x) is continuous at x=a , then limx→a​f(x) exists

If f(x) and g(x) are differentiable at x=a, then f(x)+g(x) is also differentiable at x=a

If f(x) is continuous at x=a, then it is differentiable at x=a