lim zsin lim z*. lim sin 1

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
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Chapter1: Functions
Section1.2: Functions Given By Tables
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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
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