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Determine the infinite limit.

$ \displaystyle \lim_{x \to 3^-}\frac{\sqrt{x}}{(x-3)^5} $

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02:49

Daniel Jaimes

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 2

The Limit of a Function

Limits

Derivatives

Baylor University

University of Nottingham

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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to evaluate this limit, know that we can rewrite this into limit as X approaches three from the left of square the vex times we have limits as X approaches three from the left of one over x minus three, race to the fifth power. Now from here we have the square root of three times limit as X approaches three from the left of one over x minus three to the fifth power. And from here, if X approaches three from the left, then that means that X values are less than three or that's X less than three. And this would tell us that x minus three is less than zero or the value of x minus three is negative. And so approaching three from the left would tell us that x minus three is a small negative number and becomes even smaller when raised to the fifth power. And so one over the fifth power of x minus three becomes a very large negative number. And so this is just square root of three times in negative infinity, which is the same as negative infinity. And so the value of the limit will be negative infinity.

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