Question
Asked Sep 26, 2019
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Find the limit. Show EACH STEP to justify your result. NO L'Hopital's Rule allOwed!
COs e 1
lim
202
X0
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Find the limit. Show EACH STEP to justify your result. NO L'Hopital's Rule allOwed! COs e 1 lim 202 X0

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Expert Answer

Step 1

Consider the given limit.

cos e-1
lim
202
60
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cos e-1 lim 202 60

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Step 2

Since, series expansion of cos x

cos.x 1-
+...
2!4!
6!
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cos.x 1- +... 2!4! 6!

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Step 3

So,

...
ө 05
1-
2!
-1
+.
4!
6!
lim
0
202
2!
4!
6!
lim
202
0
1
+
2!
6!
4!
lim
202
e0
+...
2!
lim
e+0
4!
6!
2
1
0-0
2!
2
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ө 05 1- 2! -1 +. 4! 6! lim 0 202 2! 4! 6! lim 202 0 1 + 2! 6! 4! lim 202 e0 +... 2! lim e+0 4! 6! 2 1 0-0 2! 2

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Tagged in

Math

Calculus

Limits