What is the best method to solve the limit \lim_{x\to

painter555ui8n 2022-04-17 Answered
What is the best method to solve the limit limx(1+sin2x2)x2?
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Answers (2)

madking711kzcb
Answered 2022-04-18 Author has 9 answers
Hint:
limx(1+sin2x2)x2=(limx(1+sin2x2)1sin(2x2))2limxsin2x22x2
Now for the exponent set 2x2=hh0+
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chabinka61jx
Answered 2022-04-19 Author has 12 answers
For questions like this one, I've found asymptotic calculations to be handy. For example:
(1+sin2x2)x2=ex2ln(1+sin2x2)=ex2(sin2x2+o(sin2x2))=ex2(2x2+o(2x2)+o(2x2))=e2+o(1)e2(x)
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