I need to solve this limit without using L'Hospital's rule.

$$\lim_{x\to 0}⁡(\cos x)^\left(\frac{-4}{x^2}\right)⁡$$


closed as off-topic by TomGrubb, RRL, Scientifica, Shailesh, Leucippus Nov 14 '18 at 0:35

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – TomGrubb, RRL, Scientifica, Shailesh, Leucippus
If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ This looks like a homework problem. Have you tried anything? $\endgroup$ – Robert Thingum Nov 13 '18 at 20:23
  • $\begingroup$ I have solved it for a friend using l'Hospital's rule. Unfortunately, my friend is attending high school and he doesn't know this rule. I don't remember how to solve it without using l'Hospital's rule.That's why I am asking for an advice here. $\endgroup$ – Alexandra Nov 13 '18 at 20:27


$$(\cos x)^{-4/x^2}=(1-\sin^2x)^{-2/x^2}=\left(\left(1-{1\over\csc^2x} \right)^{\csc^2x}\right)^{-2\left(\sin x\over x\right)^2}$$

Can you (and/or your friend) take it from there?

  • $\begingroup$ Yes! Thank you very much! $\endgroup$ – Alexandra Nov 13 '18 at 21:18

Not the answer you're looking for? Browse other questions tagged or ask your own question.