Evaluate the following limit or explain why it does not exist. 1 X lim (x + cos x)* x-0 Select the correct choice below and, if necessary, fill in any answer boxes to complete your choice. O A. 1 1 L = lim In (x + cos x) is finite and therefore lim (x + cos x) can be written as the expression x-0 x-0 OB. 1 This implies that lim (x + cos x)* = (Type an exact answer in simplified form.) x→0 The limit does not exist because it has the indeterminate form 0° which cannot be written in the form (Type an expression using L as the variable.) 0 ∞ ∞ olc O C. The limit does not exist because it has the indeterminate form 100 which cannot be written in the form or so that l'Hôpital's rule can be applied. 0 olo 0 or 88 O D. 0 ∞ The limit does not exist because it has the indeterminate form ∞o which cannot be written in the form or 0 ∞ so that l'Hôpital's rule can be applied. so that l'Hôpital's rule can be applied.

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter3: The Derivative
Section3.2: Continuity
Problem 32E
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Evaluate the following limit or explain why it does not exist.
X
lim (x + cos x)
X→0
Select the correct choice below and, if necessary, fill in any answer boxes to complete your choice.
D.
1
1
X
L = lim - In (x + cos x) is finite and therefore lim (x + cos x) can be written as the expression (Type an expression using L as the variable.)
X
X→0
X→0
1
X
This implies that lim (x + cos x) =
X→0
(Type an exact answer in simplified form.)
O B.
The limit does not exist because it has the indeterminate form 0° which cannot be written in the form
The limit does not exist because it has the indeterminate form 100 which cannot be written in the form
olo
olo
or
0
The limit does not exist because it has the indeterminate form ∞ which cannot be written in the form
0
818
or
or
88
8 8
so that l'Hôpital's rule can be applied.
so that l'Hôpital's rule can be applied.
so that l'Hôpital's rule can be applied.
Transcribed Image Text:Evaluate the following limit or explain why it does not exist. X lim (x + cos x) X→0 Select the correct choice below and, if necessary, fill in any answer boxes to complete your choice. D. 1 1 X L = lim - In (x + cos x) is finite and therefore lim (x + cos x) can be written as the expression (Type an expression using L as the variable.) X X→0 X→0 1 X This implies that lim (x + cos x) = X→0 (Type an exact answer in simplified form.) O B. The limit does not exist because it has the indeterminate form 0° which cannot be written in the form The limit does not exist because it has the indeterminate form 100 which cannot be written in the form olo olo or 0 The limit does not exist because it has the indeterminate form ∞ which cannot be written in the form 0 818 or or 88 8 8 so that l'Hôpital's rule can be applied. so that l'Hôpital's rule can be applied. so that l'Hôpital's rule can be applied.
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