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Problem

Determine the infinite limit. $ \displaystyle …

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Problem 34 Easy Difficulty

Determine the infinite limit.

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


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02:49

Daniel Jaimes

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Calculus 1 / AB

Calculus: Early Transcendentals

Chapter 2

Limits and Derivatives

Section 2

The Limit of a Function

Related Topics

Limits

Derivatives

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Top Calculus 1 / AB Educators
Grace He
Caleb Elmore

Baylor University

Samuel Hannah

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Joseph Lentino

Boston College

Calculus 1 / AB Courses

Lectures

Video Thumbnail

04:40

Limits - Intro

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.

Video Thumbnail

04:40

Derivatives - Intro

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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Video Transcript

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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Calculus: Early Transcendentals

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Related Topics

Limits

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Top Calculus 1 / AB Educators
Grace He

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Caleb Elmore

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Samuel Hannah

University of Nottingham

Joseph Lentino

Boston College

Calculus 1 / AB Courses

Lectures

Video Thumbnail

04:40

Limits - Intro

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.

Video Thumbnail

04:40

Derivatives - Intro

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.

Join Course
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