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Problem

Use continuity to evaluate the limit. $ \displ…

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Problem 35 Easy Difficulty

Use continuity to evaluate the limit.

$ \displaystyle \lim_{x \to 2} x \sqrt{20 - x^2} $


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Related Courses

Calculus 1 / AB

Calculus: Early Transcendentals

Chapter 2

Limits and Derivatives

Section 5

Continuity

Related Topics

Limits

Derivatives

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Top Calculus 1 / AB Educators
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Missouri State University

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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

This is problem thirty five Stewart Calculus, eighth edition, Section two point five. Use continuity to evaluate the limit. A limit, his expertise to X multiplied by the square root of the quantity twenty minus X squared Here to the rain to recall we have the definition of continuity. Um, that if a function of its continuous a point Okay, then the limit is expert Jesse. There was a function of is equal to f A A. If we look at this function, you see that it is eh? Combination. The product of two continuous functions we have am xs one function. The square root is another function. And then within its where we also have a polynomial which is continuous on its domain. And we have no domain restrictions, especially you. X equals a rex equals two. So because we know this function is continuous, the solution to this limit will be the the foot dysfunction evaluated it too. So two times the square root twenty minutes to squared, which is two times the square root of twenty minutes for or sixteen. Just two teams for we're just going to be eight, and that is our final answer.

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Calculus: Early Transcendentals

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Related Topics

Limits

Derivatives

Top Calculus 1 / AB Educators
Catherine Ross

Missouri State University

Kayleah Tsai

Harvey Mudd College

Kristen Karbon

University of Michigan - Ann Arbor

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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