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    Limits of Functions

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    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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    Solution Summary

    The epsilon-delta definition and limit theorems are used to evaluate limits. The solution is detailed and well presented.