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Determine the infinite limit.

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

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03:10

Daniel Jaimes

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 2

The Limit of a Function

Limits

Derivatives

Campbell University

Oregon State University

Idaho State University

Boston College

Lectures

04:40

In mathematics, the limit of a function is the value that the function gets very close to as the input approaches some value. Thus, it is referred to as the function value or output value.

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

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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.

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