Evaluating \(\displaystyle\lim_{{{x}\to{0}}}{\frac{{{1}-{\cos{{x}}}}}{{{\left({2}{x}\right)}^{{2}}}}}\) I have this question in my

aidinacol7 2022-04-03 Answered
Evaluating limx01cosx(2x)2
I have this question in my book and the answer amounts to 14. I don't see how, and I think it's an error. Can you confirm it is an error?
limx01cosx(2x)2
I assume it would need to be cos2x instead.
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Answers (1)

membatas0v2v
Answered 2022-04-04 Author has 19 answers
It's indeed not correct. Simply use l'Hopital rule allow you to conclude that
limx01cos(x)(2x)2=limx01cos(x)4x2=limx0sin(x)8x=18
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