Mathematics calculus 1

Question

Determine whether f '(0) exists.

f(x) =	x2 sin 8/x
	if x ≠ 0
0		if x = 0

a)f '(0) does exist b).f '(0) does not exist which is true?

Answer 1

f'(0) = lim x→0 (x²sin8/x - 0)/(x - 0) = lim x→0 xsin8/x = 0.

So, f'(0) exist and f'(0) = 0