Can't figure out easy limit: \(\displaystyle\lim_{{{x}\to{0}^{+}}}{\frac{{{\sin{{\left({2}{x}^{{2}}\right)}}}}}{{{x}^{{3}}}}}\) I was

WesDiectstemiwxg

WesDiectstemiwxg

Answered question

2022-03-16

Can't figure out easy limit: limx0+sin(2x2)x3
I was trying to help someone with their intro calc homework but got stumped by this super easy problem. I know we can apply L'Hôpital's rule to get limx0+4cos(2x2)3x which goes to 40=+ but I think this doesn't count as a proof. What am I forgetting?

Answer & Explanation

chupablew20

chupablew20

Beginner2022-03-17Added 1 answers

You did not forget nothing.
(sin(2x2))=4xcos(2x2)
Note
limx0(sin(2x2)2x22x2x3)
Thus, our limit it's + for x0+ and its for x0

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