Evaluate the following limits using the epsilon - delta definition and the limit theorems.
a) lim {x -> 0} sin x sin (1/x^2)
b) lim {x -> Infinity} (x^3 + 1)/(x^3 cos(1/x) + x^2 - 1)
Please also show how you came up with the answer.
The epsilon-delta definition and limit theorems are used to evaluate limits. The solution is detailed and well presented.