Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Related questions
Question
Please solve for (d) as the solution (c)
Transcribed Image Text:A1.5 Compute each of the following limits and determine the corresponding rate of convergence in the
form nk (for (a) and (b)) or xk (for (c) and (d)) with some real or integer k.
3n² - 1
(a) lim
n+∞ 7n² +n+2; (b) lim (√n +1 − √√n); (c) lim
n→∞
x→0
sin x
X
; (d) lim
x→0
ex
COS X
x²
X
![(c) solution:
lim
x70 X
to lim sinu
1 sink
x
Sinx
Further
Sinx
| =
ก
거
= (08(0)
-1
lim
ㅋ sinx
ㅈ
1
Hence by(i), 1
21-21
sine-20
기쁨에 동의
13
13 +15
x
·
Let hex) = ㅎ
1-
cos x
1
|
-)
3 25
지
x
=$+
-215
L3
ㅈ
Sinx
←
+ 12시 되어 있습니다.
--- SK +
1-42-뮈찌 - - 이
huls
Note that lim h(x)=
062
[벙 L' Hospited rum]
LS
+
- - - / = 1 × ² ( + ₁ - 2 /²/2 + 1 - - ) /
[PEN
-
L3
Hence (2)| ≤M VOCE Ng (0) for some positive constant
M.
-에드mlx21 HoxtNolo)
(i)
h(x) is bounded function
⇒
in some heighbourhood of
"x=0".
sinx
19쯤에스메게르에서 [당 1개월 121=002
-lo (bc2)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F91f76606-a4d9-42f0-be0d-7b1366a5593f%2F7aabe8e6-e75c-4358-86b0-e94680fc4a2b%2F074qa5e_processed.png&w=3840&q=75)
Transcribed Image Text:(c) solution:
lim
x70 X
to lim sinu
1 sink
x
Sinx
Further
Sinx
| =
ก
거
= (08(0)
-1
lim
ㅋ sinx
ㅈ
1
Hence by(i), 1
21-21
sine-20
기쁨에 동의
13
13 +15
x
·
Let hex) = ㅎ
1-
cos x
1
|
-)
3 25
지
x
=$+
-215
L3
ㅈ
Sinx
←
+ 12시 되어 있습니다.
--- SK +
1-42-뮈찌 - - 이
huls
Note that lim h(x)=
062
[벙 L' Hospited rum]
LS
+
- - - / = 1 × ² ( + ₁ - 2 /²/2 + 1 - - ) /
[PEN
-
L3
Hence (2)| ≤M VOCE Ng (0) for some positive constant
M.
-에드mlx21 HoxtNolo)
(i)
h(x) is bounded function
⇒
in some heighbourhood of
"x=0".
sinx
19쯤에스메게르에서 [당 1개월 121=002
-lo (bc2)
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