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Problem

Use the guidelines of this section to sketch the …

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Problem 41 Medium Difficulty

Use the guidelines of this section to sketch the curve.

$ y = \arctan(e^x) $


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Related Courses

Calculus 1 / AB

Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 4

Applications of Differentiation

Section 5

Summary of Curve Sketching

Related Topics

Derivatives

Differentiation

Volume

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Top Calculus 2 / BC Educators
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04:35

Volume - Intro

In mathematics, the volume of a solid object is the amount of three-dimensional space enclosed by the boundaries of the object. The volume of a solid of revolution (such as a sphere or cylinder) is calculated by multiplying the area of the base by the height of the solid.

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06:14

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Watch More Solved Questions in Chapter 4

Problem 1
Problem 2
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Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
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
Problem 44
Problem 45
Problem 46
Problem 47
Problem 48
Problem 49
Problem 50
Problem 51
Problem 52
Problem 53
Problem 54
Problem 55
Problem 56
Problem 57
Problem 58
Problem 59
Problem 60
Problem 61
Problem 62
Problem 63
Problem 64
Problem 65
Problem 66
Problem 67
Problem 68
Problem 69
Problem 70
Problem 71
Problem 72
Problem 73
Problem 74
Problem 75
Problem 76

Video Transcript

So the domain for this one is exes, All riel and the intercepts are zero. Just have 10 pi over four. There is an even symmetry to this craft and the Assam totes. What's so for those? So the limit as X approaches infinity over function Inverse tangent E to the X. Let's pie or two. So with X approaches infinity, We have an s in tow at Why equals pi over too. And now, for the 2nd 1 limit as X approaches negative infinity of in verse 10 of e to the X. That's going to give us zero. So we have as X approaches Negative infinity, Why is going to be zero? Okay. And now let's look for increasing decreasing intervals. So why prime equals e to the X over Okay to the two X plus one. And if we dreaded to find the critical points, will see that this is inconclusive. This is inconclusive. Um, but we can look forward the con cavity. So the second derivative Well, give us negative e to the x times e to the two x minus one over e to the two x plus one squared crucial room equal zero so we can see X equals zero. That's a point we're gonna be looking at North. Second derivative test. This is F double prime, looking for Khon cavity. You see that? It's Khan gave up to the left of zero and Khan came down to the right of zero. All right, so using this information, we can graph, So we have zero pi over four. So I'm gonna say this is pi over four. So that is, um, our intercept. And we have Oh, we have an s in tow. A cz x approaches infinity. So we have y equals pi over too. All right, So if this is pi over four than pie over to must be here, all right? And then we have y equals zero, as are other Ask him to. And now our graph. Oh, so we see that this is an inflection point that's important, cause we have a switching con cavity. So here we have, um, as X approaches infinity, it's gonna go to, but it's gonna approach but not touch or ask them to at pi over too. So this is infinity. The exes are approaching infinity, so it's gonna go this way, and negative infinity will approach. Why equals zero

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Related Topics

Derivatives

Differentiation

Volume

Top Calculus 2 / BC Educators
Grace He

Numerade Educator

Caleb Elmore

Baylor University

Samuel Hannah

University of Nottingham

Joseph Lentino

Boston College

Calculus 2 / BC Courses

Lectures

Video Thumbnail

04:35

Volume - Intro

In mathematics, the volume of a solid object is the amount of three-dimensional space enclosed by the boundaries of the object. The volume of a solid of revolution (such as a sphere or cylinder) is calculated by multiplying the area of the base by the height of the solid.

Video Thumbnail

06:14

Review

A review is a form of evaluation, analysis, and judgment of a body of work, such as a book, movie, album, play, software application, video game, or scientific research. Reviews may be used to assess the value of a resource, or to provide a summary of the content of the resource, or to judge the importance of the resource.

Join Course
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