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Question
Evaluate: `lim_(x -> 0) (1 - cos 2x)/x^2`
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Solution
Given that `lim_(x -> 0) (1 - cos 2x)/x^2`
= `lim_(x -> 0) (2 sin^2x)/x^2` .......[cos 2x = 1 – 2 sin2x]
= `lim_(x -> 0) 2(sin x/x)^2`
= `2 xx 1`
= 2 .....`[because lim_(x -> 0) sinx/x = 1]`
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