Find the limit. \(\displaystyle\lim_{{{x}\rightarrow{0}^{+}}}{\frac{{\sqrt{{x}}}}{{\sqrt{{{\sin{{x}}}}}}}}\)

Anahi Solomon

Anahi Solomon

Answered question

2022-03-31

Find the limit.
limx0+xsinx

Answer & Explanation

Jadyn Gentry

Jadyn Gentry

Beginner2022-04-01Added 12 answers

Given:
limx0+xsinx
Solve:
limx0+xsinx=limx0+1sinxx
=1limx0+sinxx
=1limx0+sinxx
taking limx0+sinxx
If substituting in the limit directly, it is reduced to the indeterminate form, so apply L'Hospitals's rule
limx0+dsinxdxdxdx=limx0+cosx1=11=1
Equation (1) becomes
limx0+xsinx=11=1
The solution is 1.

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