Textbook pdf's

.
c.
–2
30
20
10
0
–10
–20
h(t)
2
y
4
4 6
t
11. a. y a c
b. x d c
12. a.
b.
6
4
2
–4 –2 0
–2
–4
–6
8
6
y
y
y = f''(x)
2
4
x
15.
g1x2 has a vertical asymptote
at x 3.
As x S 3 , g1x2 Sq.
As x S 3 , g1x2 S q.
y x is an oblique asymptote for
h1x2.
1x 321x 22
r1x2 has vertical
1x 421x 42
asymptotes at x 4 and x 4.
As x S 4 , r1x2 Sq.
As x S 4 , r1x2 S q.
As x S 4 , r1x2 S q.
As x S 4 , r1x2 Sq.
r1x2 has a horizontal asymptote
at y 1.
a 9 b 3 5 , 5
d.
e.
2
–8 –6 –4 –2
0
2 4 6 8
–2
s(t)
4
2
–4 –2
0
2 4
–2
–4
g(x)
16
x
t
13. a.
b.
4
2
–4 –2 0
–2
2
1
–4 –2 0
–1
–2
4
2
–2
0
2 4 6
–2
y
y
y = f''(x)
2
2
4
4
x
x
x
x 2 1 x 1
16. a. lim
xSq x 1 lim x
xSq1 1 x
q
x 2 2x 1
lim
xSq x 1
1x 121x 12
lim
xSq
17.
b.
lim
xSq
q
1x 12
1x 12
lim c x2 1
xSq x 1 x2 2x 1
d
x 1
x 2 1 x 2 2x 1
lim
xSq x 1
2x
lim
xSq x 1
2
lim 2
xSq
4
3
f (x)
f.
8
–16 –8
0
8 16
–8
–16
10
s(t)
8
6
4
2
t
–8 –6 –4 –2
0
–2
2 4 6
x
–4
14. a. f 1x2 and r1x2: lim f 1x2 and lim r1x2
xSq
xSq
exist.
b. h1x2: the highest degree of x in the
numerator is exactly one degree
higher than the highest degree of x
in the denominator.
c. h1x2: the denominator is defined for
all xR.
x 3
f 1x2
has vertical
1x 721x 22
Asymptotes at x 7 and x 2.
As x S 2 , f 1x2 S q.
As x S 2 , f 1x2 Sq.
As x S 7 , f 1x2 Sq.
As x S 7 , f 1x2 S q.
f 1x2 has a horizontal asymptote at
y 0.
Mid-Chapter Review,
pp. 196–197
1. a. decreasing: 1q, 22,
increasing: 12, q 2
b. decreasing: (0, 2),
increasing: 1q, 02, 12, q 2
c. increasing: 1q, 32,
13, q 2
d. decreasing: 1q, 02,
increasing: 10, q 2
2
1
–10 –8 –6 –4 –2
0
–1
–2
–3
–4
2 4 6 8 10
x
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