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Question
Evaluate: `lim_(x -> 0) (sin x - 2 sin 3x + sin 5x)/x`
Solution
Given that `lim_(x -> 0) (sin x - 2 sin 3x + sin 5x)/x`
= `lim_(x -> 0) sinx/x - (2 sin 3x)/x + (sin 5x)/x`
= `lim_(x -> 0) sinx/x - lim_(3x -> 0) 2((sin 3x)/(3x)) xx 3 + lim_(5x -> 0) ((sin 5x)/(5x)) xx 5`
= `1 - 6 + 5`
= 0
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