Find the limit and confirm using the Sandwich Theorem: lim x->infinity (1 - cosx) / (x^2)

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Mathematics

Javon Neal

1 July, 05:08

Find the limit and confirm using the Sandwich Theorem: lim x->infinity (1 - cosx) / (x^2)

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Giovanny Francis · Answer 1

We are given with the expression (1 - cos x) / (x^2) and asked to evaluate the expression to limit as theta approaches zero. In this case, we substitute first zero. cos infinity is 1. The answer is zero over zero. This is indeterminate so we derive the terms according to L'hopital's rule. The derivative is sin x / 2x. sin infinity is 1. 1/infinity is equal to zero. Hence the answer is zero.