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Problem 42 Easy Difficulty

Determine the infinite limit.

$ \displaystyle \lim_{x \to 0^+}\left( \frac{1}{x} - \ln x \right) $

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Video Transcript

to evaluate the limits As X approaches zero from the right of one over x minus Ln of X. We first write this into The limit as X approaches zero from the right of one over X the limit. As X approaches zero from the right of Helena vex. Now, for the first limit, If X approaches zero from the right then we know the X value there is a small positive number. And so the value of one over X must be approaching positive infinity. That means for the first time we have positive infinity minus for the limit of L innovex. As X approaches zero from the right, we recall the graph of al innovex and here we see that as we move closer to zero, the value of Ln of X approaches negative infinity. And so and here we have negative infinity and so infinity minus negative infinity, that's plus infinity. Or this is going to be positive infinity. And so this is the value of the limits.