Thomas Calculus 13th [Solutions]

Chapter 10 Practice Exercises 793
70.
71.
1 3 1 3
9 15 21 27 1 4
10 16 22 28
x sin x dx x x x x x x dx x x x x x dx
0 0 3! 5! 7! 9! 0 3! 5! 7! 9!
5 11 17 23 29 1
x x x x x
5 113! 17 5! 23 7! 29 9!
0
0.185330149
1/2
tan x 1/2
dx 1 x x x x x dx x x x x x x
1 x 1 3 5 7 9 11 9 25 49 81 121
0
1 1 1 1 1 1 1 1 1 1 1 0.4872223583
2 3 2 5 2 7 2 9 2 11 2 13 2 15 2 17 2 19 2 21
9 2 5 2 7 2 9 2 11 2 13 2 15 2 17 2 19 2 21 2
1 2 4 6 8 10 3 5 7 9 11 1/2
72.
1/64 1 1/64 3 5 7
1/64 1/2 5/2 9/2 13/2
tan x dx 1 x x x x dx x 1 x 1 x 1 x dx
0 x 0 x 3 5 7 0
3 5 7
3/2 7/2 11/2 15/2
1/64
2 x 2 x 2 x 2 x
2 2 2 2
3 21 55 105 0 3 8 218 55 8 105 8
3 7 11 15
0.0013020379
73.
x 3 x 5 x 2 x 4
3! 5! 3! 5!
7 x
7 1
lim 7sin x lim lim
7
x 0 e x 0 x 0
2
2x
1
2
2 2
2
3 3
2
2
2
3 2
2x
x x
2
x x
2! 3! 2! 3!
74.
2 3 2 3 3 5
1
2
2! 3! 2! 3! 3! 5! 3! 5!
1 1 2 2 2
lim e e 2
0
sin
lim lim lim 2
0 0 0
3 5 3 5
1
2
3! 5! 3! 5! 3! 5!
75.
2 2 4 4 6
1
2
2 t 2 2 1
t t
2
t t
2
t
2 4! 4! 6! 4! 6!
1 1 t 2 2cos 1t
lim lim lim lim lim
t 0
2 2cost t t 0 t t12
t 0 t 0 t 0
2 2
2 (1 cos )
2 2 4 4 2
6
2
2
2t
1 1
t t
t
t
1
t
2 4! 4! 4!
76.
2 4 2 4 2 2 4 4 6 6
sin h
1
h h
1
h h h h h h h h
cos h
h
3! 5! 2! 4! 2! 3! 5! 4! 6! 7!
2 2 2
lim lim lim
h 0 h h 0 h h 0
h
2 2 4 4
lim 1 1 h h h h 1
h 0
2! 3! 5! 4! 6! 7! 3
77.
2 4 2 4 2
1 1 z
z
z
z
1
z
2 3 3 3
lim 1 cos z
0
ln(1 ) sin
lim lim lim 2
z
z z
z 0 z
z 0 z 0
z
2
z
3 3 5 2
2
3 4
1 2
2
z
z z z z z z z
2 3 3! 5! 2 3 4 2 3 4
78.
2 2 2
y y y
lim lim lim lim 1 1
y 0
cos y cosh y
y 0 1 1 y 0 y 0 1
y
2
y
4
y
6
y
2
y
4
y
6
2 y
2
2 y
6
2 y
4
2 4! 6! 2! 4! 6! 2 6! 6!
79.
(3 x) 3
(3 x)
5
6 120 2
3x
lim sin 3x
r s lim r s lim 3 9 81x
r
3 2 3 2 2 2 40
2
x 0 x x x 0 x x x 0 x x
s 0
r
x
2 2
3 0
x
and s 9 0 r 3 and s 9
2
2
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