I need to solve this limit: \lim_{x \to 0} \cos x^{\frac{1}{\sin

prsategazd 2021-12-30 Answered
I need to solve this limit:
limx0cosx1sinx
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Expert Answer

raefx88y
Answered 2021-12-31 Author has 26 answers

1.Call this function f(x)
2. Evaluate the limit
L=limx0logf(x)=limx0log((cosx)1sinx)=limx0(logcosx)sinx - this is a 0/0 indeterminate form but you can apply L'Hôpital to get
limx0(1cosx)sinxcosx=limx0sinxcos2x=0
The answer is eL=e0=1

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sonorous9n
Answered 2022-01-01 Author has 34 answers

Hint:
limx0(cosx)1sinx
=limx0(1sin2x)12sinx
=(limx0(1sin2x)1sin2x)limx0sinx2

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Vasquez
Answered 2022-01-09 Author has 460 answers

When
(cosx)1sinx
is meant
limx0cosx1sinx=elimx0lncosxsinx=elimx0xlncosxxsinx=elimx0lnxcosxx=elimx0(cosx1)ln(cosx+11)(cosx1)xv=elimx0cosx1x=e0=1

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