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Question
Evaluate: `lim_(x -> 0) (sin^2 2x)/(sin^2 4x)`
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Solution
Given that `lim_(x -> 0) (sin^2 2x)/(sin^2 4x)`
= `lim_(x -> 0) (sin^2 2x)/(sin^2 2(2x))`
= `lim_(x -> 0) (sin^2 2x)/(4 sin^2 2x * cos^2 2x)` ......[sin 2x = 2 sin x cos x]
= `1/(4 cos^2 2x)`
Taking limit we have
= `1/(4 * cos^2 0)`
= `1/4`
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