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Show all the steps and explain. Don't skip steps and please clear hand written f(x)=x^m sin(1/x^n)...

Show all the steps and explain. Don't skip steps and please clear hand written

f(x)=x^m sin(1/x^n) if x is not equal 0 and f(x)=0 if x =0

(a) prove that when m>1+n, then the derivative of f is continuous at 0

limit x to 0 x^n sin(1/x^n) does not exist? but why??? please explain it should be 0*sin(1/x^n)

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