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

sanuluy

sanuluy

Answered question

2021-01-30

Evaluate the following limits: limy01cos(7y)2y

Answer & Explanation

yagombyeR

yagombyeR

Skilled2021-01-31Added 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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