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Limit of cosine using epsilon/delta definition

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I am having difficulty using the epsilon/delta definition....even difficulty when not using it. There's a problem which reads as follows: find the limit as x approaches 0 of (cosx-1)/x^2. The main reason as to why I am having difficulty without using the epsilon/delta definition is because I simply am confused what to do when x goes to zero, yet it is in the denominator. I don't even know where to begin using the epsilon/delta definition! Please help! Another problem that is similar is: limit as h approaches zero of ((e^h)-1)/h and limit as x approaches zero of ((sin^2)x)/x.

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Evaluating Limits: Epsilon-Delta Definition and Limit Theorems

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.

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