Problem

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

View

Problem 40 Easy Difficulty

Find the limit or show that it does not exist.

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

Answer

$=-\frac{\pi}{2}$

Topics

Limits

Derivatives

Calculus: Early Transcendentals

Chapter 2

Limits and Derivatives

Section 6

Limits at Infinity: Horizontal Asymptotes

Discussion

You must be signed in to discuss.

Top Calculus 1 / AB Educators

Watch More Solved Questions in Chapter 2

Problem 1

Problem 2

Problem 3

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.

Daniel J.