260 EXERCISE Evaluate each of the following limits. 1. lim x ln x. 2-0 Ans. *0. 1. 3. lim x csc 2x. 1-0 5. lim xel/z. 2-04 7. lim csc x Sin-¹ x. 2-0 9. lim tan x tan 2x. Inc T 8 1. -2.
260 EXERCISE Evaluate each of the following limits. 1. lim x ln x. 2-0 Ans. *0. 1. 3. lim x csc 2x. 1-0 5. lim xel/z. 2-04 7. lim csc x Sin-¹ x. 2-0 9. lim tan x tan 2x. Inc T 8 1. -2.
Calculus: Early Transcendentals
8th Edition
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Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
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calculus with analytic geometry by thurman S. Peterson
![260
5. lim xel/z.
7. lim csc x Sin-¹ x.
9. lim tan x tan 2x.
II. lim (secx - tan x).
(-)
15. lim (tan 5x - tan x).
17. lim (csc x
csc 2x).
Evaluate each of the following limits.
1. lim x ln x.
Ans. *0.
3. lim x csc 2x.
t.
13. lim
-
23. lim
2-0
19. lim
2-0
21. lim (ex - x).
sin x)
Indeterminate Forms
1
(sin³² x - - 2).
EXERCISE 56
∞0.
1.
-2.
0.
-1.
8.
00.
0.
∞.
3.
2. lim x sin (π/x).
218
4.
lim sec 5x cos 3x.
x²
6.
lim
2-1
x
x⁹-1
8. lim sin x ln (tan x).
10.
12.
14.
16.
18.
x→0
lim (1
lim
x-1
x? 1
lim
211
lim
lim [ln (x-2)
818
1
24. lim
241
x
tan x) sec 2x.
x 1
-
-
In x
(x tan x
n
1
20. lim
x sin x
x-0
22. lim [In x
P18
-
1
x ln x
-
5
-
FX).
3)
In (In x)].
Inx].
In y = g(x) In f(x).
If we find that lim In y = k, it follows that lim y = e.
Example I F
1 xm
sec x).
m
120. The Indeterminate Forms 0⁰, ∞ 0, 1 ∞
If f(x) → 0 and g(x) →0, or f(x) → ∞o and g(x) → 0, or f(x)→
1 and
g(x) → ∞ as x→a (or x→ + ∞0), the expression f(a)s (a) is undefined
and is said to assume the indeterminate form 00, 000, or 1%, respectively.
If the limit of f(x)(a) exists as x→a (or x ±00), it may be found by
denoting the expression by y, and investigating the limit approached
by the logarithm](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0f19b9fc-b344-4a0b-b6da-0671359fef14%2F323bdef2-fe05-4ca4-a846-19c095f23474%2Fjvilce_processed.jpeg&w=3840&q=75)
Transcribed Image Text:260
5. lim xel/z.
7. lim csc x Sin-¹ x.
9. lim tan x tan 2x.
II. lim (secx - tan x).
(-)
15. lim (tan 5x - tan x).
17. lim (csc x
csc 2x).
Evaluate each of the following limits.
1. lim x ln x.
Ans. *0.
3. lim x csc 2x.
t.
13. lim
-
23. lim
2-0
19. lim
2-0
21. lim (ex - x).
sin x)
Indeterminate Forms
1
(sin³² x - - 2).
EXERCISE 56
∞0.
1.
-2.
0.
-1.
8.
00.
0.
∞.
3.
2. lim x sin (π/x).
218
4.
lim sec 5x cos 3x.
x²
6.
lim
2-1
x
x⁹-1
8. lim sin x ln (tan x).
10.
12.
14.
16.
18.
x→0
lim (1
lim
x-1
x? 1
lim
211
lim
lim [ln (x-2)
818
1
24. lim
241
x
tan x) sec 2x.
x 1
-
-
In x
(x tan x
n
1
20. lim
x sin x
x-0
22. lim [In x
P18
-
1
x ln x
-
5
-
FX).
3)
In (In x)].
Inx].
In y = g(x) In f(x).
If we find that lim In y = k, it follows that lim y = e.
Example I F
1 xm
sec x).
m
120. The Indeterminate Forms 0⁰, ∞ 0, 1 ∞
If f(x) → 0 and g(x) →0, or f(x) → ∞o and g(x) → 0, or f(x)→
1 and
g(x) → ∞ as x→a (or x→ + ∞0), the expression f(a)s (a) is undefined
and is said to assume the indeterminate form 00, 000, or 1%, respectively.
If the limit of f(x)(a) exists as x→a (or x ±00), it may be found by
denoting the expression by y, and investigating the limit approached
by the logarithm
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