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If m>1 then x^m sin(1/x^n) will be differentiable at 0 However, why? Q1. if we take...

If m>1 then x^m sin(1/x^n) will be differentiable at 0

However, why?

Q1. if we take limit x to 0 sin(1/x^n), we get sin(1/0) it doesn't make sense even if m>1

Q2. why when M=1, it will not differentiable at 0?

Q3 Please tell me that limit x to infinity sin(1/x) DNE becasue limit will be -1 and 1???? is that the reason?

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