Calculus

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Find the positive integers k for which
lim ->0 sin(sin(x))/x^k

exists, and then find the value the limit.
(hint:consider first k=0, then k=1. Find the limit in these simple cases. Next take k=2 and finally consder k>2 and find the limit in these cases as well)

I did this for the first one
lim x->0 sin(sinx))/x^0=0

then idk how to do the other ones

  • Calculus -

    k=1 limit sinx/x=1
    k=2 limit sinx/x *1/x= undefined
    and so on.

  • Calculus -

    for k=2 lim x->0 sin(sin(x))/x^2= error
    so undefined So do I have to do sided limits? how?

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