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# Determine the infinite limit.$\displaystyle \lim_{x \to (\pi/2)^+}\frac{1}{x}\sec x$

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

Limits

Derivatives

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##### Catherine R.

Missouri State University

##### Kristen K.

University of Michigan - Ann Arbor

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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.

DM
Oklahoma State University

#### Topics

Limits

Derivatives

##### Catherine R.

Missouri State University

##### Kristen K.

University of Michigan - Ann Arbor

Lectures

Join Bootcamp