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Limit of cosine using epsilon/delta definition

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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This solution is comprised of a detailed explanation to answer limit of cosine using epsilon/delta definition.