Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.3: The Natural Exponential Function
Problem 56E
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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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa339e260-85b6-4ffe-ac43-149e8338d348%2Fcbcb6116-c952-4242-a9f5-87ad8a487f86%2Ftw68vk_processed.png&w=3840&q=75)
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
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