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(a) By graphing the function $ f(x) = (\cos 2x - …

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Problem 28 Easy Difficulty

Use a table of values to estimate the value of the limit. If you have a graphing device, use it to confirm your result graphically.

$ \displaystyle \lim_{x \to 0^+}x^2 \ln x $


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Related Courses

Calculus 1 / AB

Calculus: Early Transcendentals

Chapter 2

Limits and Derivatives

Section 2

The Limit of a Function

Related Topics

Limits

Derivatives

Discussion

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Top Calculus 1 / AB Educators
Heather Zimmers

Oregon State University

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Harvey Mudd College

Kristen Karbon

University of Michigan - Ann Arbor

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Idaho State University

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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Watch More Solved Questions in Chapter 2

Problem 1
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Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
Problem 26
Problem 27
Problem 28
Problem 29
Problem 30
Problem 31
Problem 32
Problem 33
Problem 34
Problem 35
Problem 36
Problem 37
Problem 38
Problem 39
Problem 40
Problem 41
Problem 42
Problem 43
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Problem 46
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Problem 48
Problem 49
Problem 50
Problem 51
Problem 52
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Problem 55

Video Transcript

This is problem A number twenty eight Stuart Calculus, eighth Edition, section two point two. Use table values to estimate the value of the limit. If you have a graphing device, easy to confirm your result graphically. The limit as X approaches zero from the right of the function X squared Tamil Allen of X for this problem, since it's a limit as experts zero from the right or from the positive side, we will only be choosing values that are positive. Ah, and very small, very closer to zero. As you can see in our table, we have chosen values such a zero point five zero point one and getting increasingly smaller but still larger than zero. And if we look at the calculations done using the function given using each of these X's valleys, we see that the value is that negative number in this range and gets increasingly smaller, increasingly closer to zero. Here, we're very, very close to zero. And what we can estimate at this point is that the limit as X approaches zero from the right is that this function will approach it. Zero. We're going to confirm our result graphically using a plot in the spreadsheet. You can also use a graphing calculator or another graphing tool and plus X squared times E clinics around X equals zero, but not to the left on ly to the right as we're looking for the limit as experts, zero from the right and as we see from the right, the function this whole stream closer to zero as Ex gets closer and closer to zero, and with his confirmation, we can conclude that dis limit is equal to zero.

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Calculus: Early Transcendentals

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Related Topics

Limits

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Top Calculus 1 / AB Educators
Heather Zimmers

Oregon State University

Kayleah Tsai

Harvey Mudd College

Kristen Karbon

University of Michigan - Ann Arbor

Michael Jacobsen

Idaho State University

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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