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DM
Numerade Educator

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Problem 37 Medium Difficulty

Determine the infinite limit.

$ \displaystyle \lim_{x \to (\pi/2)^+}\frac{1}{x}\sec x $

Answer

$$-\infty \text { as } x \rightarrow(\pi / 2)^{+}$$

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Video Transcript

So in this problem were asked to evaluate the limit as X approaches by over two from the right of one over X second X remember seeking ex is one over the co sign of X. So this is the limit As X approaches pi over two from the right of one over X. Co sign X. Okay. Now remember that limit As X approaches pi over two of cosign X is zero. So this means I am going to be dividing bye zero, aren't I? And so therefore the limit as x approaches pi over two from the right one over X second X is going to be minus infinity. Okay, Because as I approach by over two, I hear this one, let's say I did this I said X approaches pi over two from the right one over co sign X. Who to assign X. Well, Co sign X approaches zero. So I'm getting a smaller and smaller and smaller number. And so this is infinity. It's actually heading towards negative infinity. Remember our second graf. And so therefore that whole limit is negative infinity.