-1 Use the Taylor series for sinh x and coshx to verify that 5 Use che Tayior series for co COS JT 0. tulll X cosh x. sinh x What condition must be met by a function f for it to have a Taylor series centered at a? 7-24. Limits Evaluate the following limits using Taylor series. X - x,_ue) Practice Exercises -1. lim e- 1 lim 8 7. O-r 0-r X sin 2x (r- I)- 10. lim 9. lim 0-r X 1 + x - e e- e 12. lim 11. lim O-r 4x2 0-r X 2 cos 2x - 2 +4r2 T 14. lim x sin 13. lim 2r4 0-r 00-x X In (1 + x)- x+ x/2 x2- 16 15. lim 16. lim *-4 In (x 3) 3 3 tan x 3x + x 17. lim 18. lim 0-r 4x2 (7/x)- I-x + IA 0-1 19. lim 12x- 8x- 6 sin 2x x - 1 20. lim x-1 In x 0-r 21. lim x-2 -2 In (x - 1) 22. lim x(elx (I- (1 2x)-1/2 23. lim /x 2x2 00-X 3 24. lim Use the Taylor se cosh x. 6 What condition must be met by a function series centered at a? 7-24. Limits Evaluate the following limits using tan Practice Exercises 8. lim 7. lim I - OX 0-x x -x-In (1- x) sin 10. lim 9. lim 0-X 11. lim 12. lim I 2 cos 2x - 2 4x2 13. lim 14. lim x 0-r 2r4 o0x In (1 + x)-x + x - x + x/2 15. lim 16. lim 0-1 3 tan x 3x +x 17. lim - X,_ue c 0-r 18. lim 12x 19. lim 8x-6 sin 2x 0-x 0-r 20. lim X
-1 Use the Taylor series for sinh x and coshx to verify that 5 Use che Tayior series for co COS JT 0. tulll X cosh x. sinh x What condition must be met by a function f for it to have a Taylor series centered at a? 7-24. Limits Evaluate the following limits using Taylor series. X - x,_ue) Practice Exercises -1. lim e- 1 lim 8 7. O-r 0-r X sin 2x (r- I)- 10. lim 9. lim 0-r X 1 + x - e e- e 12. lim 11. lim O-r 4x2 0-r X 2 cos 2x - 2 +4r2 T 14. lim x sin 13. lim 2r4 0-r 00-x X In (1 + x)- x+ x/2 x2- 16 15. lim 16. lim *-4 In (x 3) 3 3 tan x 3x + x 17. lim 18. lim 0-r 4x2 (7/x)- I-x + IA 0-1 19. lim 12x- 8x- 6 sin 2x x - 1 20. lim x-1 In x 0-r 21. lim x-2 -2 In (x - 1) 22. lim x(elx (I- (1 2x)-1/2 23. lim /x 2x2 00-X 3 24. lim Use the Taylor se cosh x. 6 What condition must be met by a function series centered at a? 7-24. Limits Evaluate the following limits using tan Practice Exercises 8. lim 7. lim I - OX 0-x x -x-In (1- x) sin 10. lim 9. lim 0-X 11. lim 12. lim I 2 cos 2x - 2 4x2 13. lim 14. lim x 0-r 2r4 o0x In (1 + x)-x + x - x + x/2 15. lim 16. lim 0-1 3 tan x 3x +x 17. lim - X,_ue c 0-r 18. lim 12x 19. lim 8x-6 sin 2x 0-x 0-r 20. lim X
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...
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Can you help me on #11.
Transcribed Image Text:-1
Use the Taylor series for sinh x and coshx to verify that
5
Use che Tayior series for co
COS JT
0.
tulll
X
cosh x.
sinh x
What condition must be met by a function f for it to have a Taylor
series centered at a?
7-24. Limits Evaluate the following limits using Taylor series.
X - x,_ue)
Practice Exercises
-1.
lim
e- 1
lim
8
7.
O-r
0-r
X
sin 2x
(r- I)-
10. lim
9.
lim
0-r
X
1 + x - e
e- e
12. lim
11. lim
O-r
4x2
0-r
X
2 cos 2x - 2 +4r2
T
14. lim x sin
13. lim
2r4
0-r
00-x
X
In (1 + x)- x+ x/2
x2- 16
15. lim
16. lim
*-4 In (x 3)
3
3 tan x 3x + x
17. lim
18. lim
0-r
4x2
(7/x)- I-x + IA
0-1
19. lim
12x- 8x- 6 sin 2x
x - 1
20. lim
x-1 In x
0-r
21. lim
x-2
-2 In (x - 1)
22. lim x(elx
(I-
(1 2x)-1/2
23. lim
/x
2x2
00-X
3
24. lim
Transcribed Image Text:Use the Taylor se
cosh x.
6
What condition must be met by a function
series centered at a?
7-24. Limits Evaluate the following limits using
tan
Practice Exercises
8.
lim
7. lim
I -
OX
0-x
x
-x-In (1- x)
sin
10. lim
9. lim
0-X
11. lim
12. lim
I
2 cos 2x - 2 4x2
13. lim
14. lim x
0-r
2r4
o0x
In (1 + x)-x + x
- x + x/2
15. lim
16. lim
0-1
3 tan x 3x +x
17. lim
- X,_ue c
0-r
18. lim
12x
19. lim
8x-6 sin 2x
0-x
0-r
20. lim
X
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