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