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Find the limit or show that it does not exist. …

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Problem 40 Easy Difficulty

Find the limit or show that it does not exist.

$ \displaystyle \lim_{x \to 0^+} \tan^{-1}(\ln x) $


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Related Courses

Calculus 1 / AB

Calculus: Early Transcendentals

Chapter 2

Limits and Derivatives

Section 6

Limits at Infinity: Horizontal Asymptotes

Related Topics

Limits

Derivatives

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Top Calculus 1 / AB Educators
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Missouri State University

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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
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 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
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
Problem 77
Problem 78
Problem 79
Problem 80
Problem 81

Video Transcript

this problem Number forty of the Stuart can't close a tradition section two point six I'm the limit or showed that it does not exist. Limited's experts zero from the right with the function tangent inverse of Alan of X. Now we use a property of limits where if you have a function within a function, this can also be represented as he outer function or the limit now inside of the outer function applied to the inter function. So he righted a such that we can solve this limit by solving love it on the inside and then applying it to be outer function afterward. So let's recall the grass of the function Ellen and interest Tangent. Yellen function is of this form and as it approaches here from the right, uh, as you can see it, a purchase Negative. Infinity, for this limit we know is perching negative infinity. So Denver just towards negative infinity and the universe tension function Looks like this with a horizontal Ask himto at positive, however too. And a negative carver too. So for the inverse tangent function, if we had an input, it's argument is coin towards negative infinity, then it will be approaching negative power over too. So since this inner limit is approaching it infinity and native infinity for tension inverse purchase proper too. The answer to your original limit must be, uh, negative power, too. That is your final answer.

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Calculus: Early Transcendentals

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Related Topics

Limits

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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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