Find the limit. lim_{xrightarrow0^+}frac{sqrt x}{sqrt{sin x}}

Burhan Hopper 2020-11-23 Answered
Find the limit.
limx0+xsinx
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Expert Answer

Clelioo
Answered 2020-11-24 Author has 88 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 LHospitalss rule
limx0+dsinxdxdxdx=limx0+cosx1=11=1
Equation (1) becomes
limx0+xsinx=11=1
The solution is 1.
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