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Question
Evaluate the following limits:
`lim_(x -> pi) (sin3x)/(sin2x)`
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Solution
`lim_(x -> pi) (sin3x)/(sin2x) = lim_(x -> pi) (3sin x - 4 sin^3 x)/(2sinx cos x)`
= `lim_(x -> pi) [(3sinx)/(2sinx cosx) - (4sin^3x)/(sinx cosx)]`
= `lim_(x -> pi) [3/(2cosx) - (2sin^2x)/cosx]`
= `lim_(x -> pi) 3/(2cosx) - lim_(x -> pi) (2sin^2x)/cosx`
= `3/(2cospi) - (2sin^2pi)/cospi`
=`3/(2 xx -1) - (2 xx 0)/(-1)`
`lim_(x -> pi) (sin3x)/(sin2x) = - 3/2`
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