Constantine
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- Jul 17, 2016
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Hello, I have a question regarding using l'Hospital's Rule to solve problems with indeterminate powers. The specific problem which comes from my textbook is given below:
x→0lim(1+sin(4x))cot(x)
ln(y)=ln[(1+sin(4x))cot(x)]
ln(y)=cot(x)ln(1+sin(4x))
x→0limln(y)=x→0limtan(x)ln(1+sin(4x))=x→0limsec2(x)(1+sin(4x)4cos(4x))=4
x→0lim(1+sin(4x))cot(x)=e4
I understand how to use the Rule but what I don't get is how cotx function from step #3 became tanx function found in the denominator in the following step. I have tried solving the problem numerous times on my own but I don't understand how tanx got there. If somebody could please explain that to me, I would be very grateful.
Thank you,
Constantine
x→0lim(1+sin(4x))cot(x)
ln(y)=ln[(1+sin(4x))cot(x)]
ln(y)=cot(x)ln(1+sin(4x))
x→0limln(y)=x→0limtan(x)ln(1+sin(4x))=x→0limsec2(x)(1+sin(4x)4cos(4x))=4
x→0lim(1+sin(4x))cot(x)=e4
I understand how to use the Rule but what I don't get is how cotx function from step #3 became tanx function found in the denominator in the following step. I have tried solving the problem numerous times on my own but I don't understand how tanx got there. If somebody could please explain that to me, I would be very grateful.
Thank you,
Constantine
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