What is limit of (sinx)^(tgx) if x --->0?

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You need to replace 0 for x to evaluate the limit, such that:

`lim_(x->0) (sin x)^tan x = (sin 0)^(tan 0) = 0^(0) = 0`

The indetermination `0^0` requests for you to use l'Hospital's theorem, such that:

`lim_(x->0) (sin x)^tan x = lim_(x->0) e^(ln (sin x)^tan x)`

Using power property of logarithms yields:

`lim_(x->0) e^(ln...

(The entire section contains 197 words.)

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