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Question
Evaluate: `lim_(x -> pi/4) (sin x - cosx)/(x - pi/4)`
Solution
Given that `lim_(x -> pi/4) (sin x - cosx)/(x - pi/4)`
= `lim_(x -> pi/4) (sqrt(2)(1/sqrt(2) sin x - 1/sqrt(2) cos x))/(x - pi/4)`
= `lim_(x -> pi/4) (sqrt(2) (cos pi/4 sin x - sin pi/4 cos x))/(x - pi/4)`
= `lim_((x -> pi/4),(because x - pi/4 -> 0)) (sqrt(2) sin (x - pi/4))/(x - pi/4)`
`sqrt(2) * 1 = sqrt(2)`
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