If f x = x 2 sin 1 x , when x ≠ 0 and f 0 = 0 , then lim x → 0 f ' x

Question

If f x = x 2 sin 1 x , when x ≠ 0 and f 0 = 0 , then lim x → 0 f ' x, Does not exist, 0, ∞, 1

MARKS App · Accepted Answer

lim x → 0 f ' x = lim x → 0 2 x sin 1 x + x 2 - 1 x 2 cos 1 x = 2 lim x → 0 x sin 1 x - lim x → 0 cos 1 x = 0 - lim x → 0 cos 1 x Limit does not exist as value of cos 1 x oscillatesy between - 1 & 1 as x approaches 0 .

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