Evaluate the following limits lim_{xrightarrow0}frac{sin7x}{sin3x}

Dolly Robinson 2020-11-10 Answered
Evaluate the following limits
limx0sin7xsin3x
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Expert Answer

casincal
Answered 2020-11-11 Author has 82 answers
We have to evaluate the limit:
limx0sin7xsin3x
We know that
limx0sinxx=1
if limx0sinaxx
in this case we need to multiply and divide by a since we do make same in the denominator as in the angle of sine.
limx0sinaxx×=limx0sinaxax×a
=1×a
=a
if limx0sinaxsinbx
then same case will be for numerator and denominator.
hence,
limx0sinaxsinbx=ab
Finding given limit:
here, a=7
b=3
Hence,
limx0sin7xsin3x=73
Second method:
Multiplying and dividing by 7x for numerator and by 3x for denominator, we get
limx0sin7xsin3x×7x7x×3x3x=limx0sin7x7x3x3x×7x1×13x
=11×71×13
=73
Hence, value of the given limit is 73
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Jeffrey Jordon
Answered 2022-04-01 Author has 2047 answers

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