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Suppose that functions $f$ and $g$ are differenti…

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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 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 69 Hard Difficulty

Find $\lim _{x \rightarrow 0^{+}} \frac{x \sin (1 / x)}{\sin x}$ if it exists.

Answer

$=1 \cdot$ A finite (but not fixed) quantity between -1 and 1 the limit does not exist.

Related Courses

Calculus 1 / AB

Calculus Early Transcendentals

Chapter 3

TOPICS IN DIFFERENTIATION

Section 6

L Hopital's Rule; Indeterminate Forms

Related Topics

Functions

Limits

Derivatives

Differentiation

Continuous Functions

Applications of the Derivative

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Problem 16

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Problem 20

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Problem 24

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Problem 27

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Problem 30

Problem 31

Problem 32

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Problem 36

Problem 37

Problem 38

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Problem 40

Problem 41

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Problem 46

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Problem 48

Problem 49

Problem 50

Problem 51

Problem 52

Problem 53

Problem 54

Problem 55

Problem 56

Problem 57

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Problem 59

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Problem 69

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Problem 72

Video Transcript

we have the limits as X goes to zero from the positive side of X Sign of one over X divided by sine X. Now, one of things we can do is split this up. Um, here, we're going to assume that the limit does exist so that we can split up, split it up into two limits. Notice that this first limit Now we can apply low petals rule because we get 0/0. The second limit stays the same. Okay, the first limit is equal toe one. And because it is a finite non zero number, it follows that this limit does not exist because sign is oscillating me to negative one and one.

We have video lessons for 84.11% of the questions in this textbook

Howard Anton, Irl Bivens, Stephen Davis

Calculus Early Transcendentals

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Related Topics

Functions

Limits

Derivatives

Differentiation

Continuous Functions

Applications of the Derivative

Top Calculus 1 / AB Educators

Catherine R.

Missouri State University

Samuel H.

University of Nottingham

Michael J.

Idaho State University

Joseph L.

Boston College

Calculus 1 / AB Courses

Lectures

Video Thumbnail

03:09

Precalculus Review - Intro

In mathematics, precalculus is the study of functions (as opposed to calculu…

Video Thumbnail

31:55

Functions on the Real Line - Overview

In mathematics, a function (or map) f from a set X to a set Y is a rule whic…

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Find the limit.
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Find the limit.
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Find the limits.
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