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Question
Evaluate the following limits:
`lim_(x -> 0) (sin^3(x/2))/x^2`
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Solution
We know `lim_(x -> 0) sinx/x` = 1
`lim_(x -> 0) (sin^3(x/2))/x^3 = lim_(x -> 0) (sin^3(x/2))/(2^3 xx x^3/2^3)`
= `lim_(x/2 -> 0) 1/8* (sin^3(x/2))/(x/2)^3`
= `1/8 lim_(x/2 -> 0) [(sin (x/2))/(x/2)]^3`
`lim_(x -> 0) (sin^3(x/2))/x^2 = 1/8 xx 1^3`
= `1/8`
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