Sunday, January 14, 2018

calculus - $lim_{x rightarrow 0}left(frac{1}{sin^2(x)} -frac{1}{x^2}right)$ and the problem of $infty-infty$

I'm trying to calculate




$$\lim_{x \rightarrow 0}\left(\frac{1}{\sin^2(x)} -\frac{1}{x^2}\right)$$



but I'm having the problem of getting



$$\infty - \infty$$



which I read to be indeterminate.



I cannot figure out how could I manipulate the above to get rid of the indeterminacy.

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