lim zsin lim z*. lim sin 1

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
icon
Related questions
Topic Video
Question

I'm not understanding the squeeze theorem. 

O Lumen OHM
2-2-example-04.gif (88 x
6 2-3-ex-10-alt.gif (857x
| Simplify tan(x)cos(x) | M
M. Limit Laws explained w
w Squeeze theorem - Wik x
+
A https://ohm.lumenlearning.com/assess2/?cid=50238&aid=3647337#/skip/14
I Apps M McGraw-Hill Conne.
E Program: Chemistry. P Employee Self-Servi. Q Lumen OHM
Courses in Chemist...
FIrst hote that we ca not use
1
lim x sin
1
lim z4. lim sin
because the limit as x approaches 0 of sin
1
does not exist (see this example 2). Instead we apply
1
the Squeeze Theorem, and so we need to find a function f smaller than g(x)
= x' sin
and a
function h bigger than g such that both f(x) and h(x) approach 0. To do this we use our
knowledge of the sine function. Because the sine of any number lies between -1
and
1
o, we can write
1
< sin
-1
Any inequality remains true when multiplied by a positive number. We know that a* > 0 for all æ
and so, multiplying each side of inequalities of æ*, we get
sin
as illustrated by the figure. We know that
lim x*
and lim
1
Taking f(x) = – a*, g(æ)
= x* sin –, and h(x) = x* in the Squeeze Theorem, we obtain
lim a* sin
1
= 0.
4:37 PM
P Type here to search
99+
2/14/2021
近
Transcribed Image Text:O Lumen OHM 2-2-example-04.gif (88 x 6 2-3-ex-10-alt.gif (857x | Simplify tan(x)cos(x) | M M. Limit Laws explained w w Squeeze theorem - Wik x + A https://ohm.lumenlearning.com/assess2/?cid=50238&aid=3647337#/skip/14 I Apps M McGraw-Hill Conne. E Program: Chemistry. P Employee Self-Servi. Q Lumen OHM Courses in Chemist... FIrst hote that we ca not use 1 lim x sin 1 lim z4. lim sin because the limit as x approaches 0 of sin 1 does not exist (see this example 2). Instead we apply 1 the Squeeze Theorem, and so we need to find a function f smaller than g(x) = x' sin and a function h bigger than g such that both f(x) and h(x) approach 0. To do this we use our knowledge of the sine function. Because the sine of any number lies between -1 and 1 o, we can write 1 < sin -1 Any inequality remains true when multiplied by a positive number. We know that a* > 0 for all æ and so, multiplying each side of inequalities of æ*, we get sin as illustrated by the figure. We know that lim x* and lim 1 Taking f(x) = – a*, g(æ) = x* sin –, and h(x) = x* in the Squeeze Theorem, we obtain lim a* sin 1 = 0. 4:37 PM P Type here to search 99+ 2/14/2021 近
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Knowledge Booster
Sequence
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning