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Question
Evaluate `lim_(x -> 0) (sin(2 + x) - sin(2 - x))/x`
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Solution
We have `lim_(x -> 0) (sin(2 + x) - sin(2 - x))/x`
= `lim_(x -> 0) (2cos ((2 + x + 2 - x))/2 sin ((2 + x - 2 + x))/2)/x`
= `lim_(x -> 0) (2cos 2sinx)/x`
= `2cos 2 lim_(x -> 0) sinx/x`
= 2cos 2 as `lim_(x -> 0) sinx/x` = 1
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