How do you find the limit of $(x^(3 sin x))$ as x approaches 0+?

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Answer 1 · 2016-09-21T13:54:45

$1$

$x^(3 sin x)equiv (1+delta)^(3sin(1+delta))$

$(1+delta)^(3sin(1+delta)) = 1 + 3sin(1+delta) delta + (3sin(1+delta)(3sin(1+delta)-1))/(2!)delta^2+cdots$

$lim_(x->0)x^(3 sin x) equiv lim_(delta->-1) (1+delta)^(3sin(1+delta)) =1$

How do you find the limit of (x^(3 sin x))(x^(3 sin x)) as x approaches 0+?