Using the definition of |x-a|<delta implies |f(x) - L|<epsilon, prove that lim x->0 x^n*sin(1/x) holds for all n belonging to natural numbers.
Definition of a limit
The Attempt at a Solution
Ok, so when I see "prove for all n belonging to natural numbers" I immediately think induction. So this is what I have done so far. For n=1 lim x->0 x^n*sin(1/x) is true; the limit is zero. Now I will assume lim x->0 x^n*sin(1/x) for some n is true, then I need to show that n+1 is also true. So I start using the definition of the limit and don't know what my L should be and how to use induction along with this definition of a limit. Please help and thank you in advanced.