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Question
Evaluate `lim_(x -> 0) (tanx - sinx)/(sin^3x)`
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Solution
We have `lim_(x -> 0) (tanx - sinx)/(sin^3x)`
= `lim_(x -> 0) (sinx 1/cosx - 1)/(sin^3x)`
= `lim_(x -> 0) (1 - cosx)/(cosx sin^2x)`
= `lim_( -> 0) (2sin^2 x/2)/(cosx 4sin^2 x/2 * cos^2 x/2)`
= `1/2`.
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