Evaluate the following limits: lim_{yrightarrow0}frac{1-cos(7y)}{2y}

sanuluy 2021-01-30 Answered
Evaluate the following limits: limy01cos(7y)2y
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Expert Answer

yagombyeR
Answered 2021-01-31 Author has 92 answers
Given:
limy01cos(7y)2y
We have to evaluate the given limit
We have,
limy01cos(7y)2y
When we substitute y=0 in given limit we get,
1cos(70)(20)=110=00
We get the indeterminate form if we substitute y=0 then we used LHospitals Rule.
LHospitals Rule :
The rule tells us that if we have an indeterminate form 00 or all we need to do is differentiate the numerator and differentiate the denominator and then take the limit.
Now differentiate the numerator and differentiate the denominator with respect to y:
limy0ddy(1cos(7y))ddy(2y)
=limy00(7sin(7y))2
=limy07sin(7y)2
=72limy0sin(7y)
=0
[limy0sin(7y)=0]
Hence, limy01cos(7y)2y=0
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