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Numerade Educator

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Problem 43 Hard Difficulty

Determine the infinite limit.

$ \displaystyle \lim_{x \to 0}(\ln x^2 - x^{-2}) $

Answer

$\lim _{x \rightarrow 0}\left(\ln x^{2}-x^{-2}\right)=-\infty \sin c e \ln x^{2} \rightarrow-\infty$ and $x^{-2} \rightarrow \infty$ as $x \rightarrow 0$

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Video Transcript

to evaluate this limit, know that we can rewrite this into limit as X approaches zero of you have to Ln of x minus one over x rays to the second power. This is because Ln of a reached um is the same as M Elena V property of natural log. And then from here evaluating at zero we get to Ln of zero minus 1/0 squared and from here we have two times negative infinity. Since the value of natural log as X approaches zero approaches negative infinity and then you have minus 1/0, which will always approach positive infinity as X goes to zero either from the left or right, so this is minus infinity and we have negative infinity minus negative infinity. This will give us evaluations negative infinity. Therefore the value of the limit is negative infinity.