Evaluate the following limits. lim_{xrightarrow0}frac{tan7x}{sin x}

Rivka Thorpe 2021-02-19 Answered
Evaluate the following limits.
limx0tan7xsinx
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Expert Answer

broliY
Answered 2021-02-20 Author has 97 answers
Given Function,
f(x)=tan7xsinx
We have to find,
limx0tan7xsinx
As we know,
If we get 00 an Indeterminate form then,
limx0f(x)g(x)=limx0f(x)g(x)
limx0tan7xsinx
We have an indeterminate form of type 00, we can apply L'Hospital Rule,
limx0tan7xsinx=limx0ddx(tan7x)ddx(sinx)
limx0tan7xsinx=limx07tan27x+7cosx
as we know,
tan2x=sec2x1
limx0tan7xsinx=limx07(sec27x1)+7cosx
=limx07sec27x7+7cosx
=limx07cosx×cos27x
put x=0
limx0tan7xsinx=71=7
Result: limx0tan7xsinx=7
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Jeffrey Jordon
Answered 2022-04-01 Author has 2047 answers

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