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Let f(x)={{:(,x^(n)"sin "(1)/(x),x ne 0)...

Let `f(x)={{:(,x^(n)"sin "(1)/(x),x ne 0),(,0,x=0):}` Then f(x) is continuous but not differentiable at x=0. If

A

`underset(x rarr 0)(lim) f(x)` exists for every `n gt 1`

B

f is continuous at x = 0 for `n gt 1`

C

f is differentiable at x= 0 for every `n gt 1`

D

None of the above

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The correct Answer is:
A, B, C
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