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x 2.
5. a. 19 000 fish>
year
b. 23 000 fish>
year
6. a. i. 3
ii. 1
iii. 3
iv. 2
b. No, lim f 1x2 does not exist. In order
xS4
for the limit to exist, lim xS4
and lim must exist and they
xS4
must be the same. In this case,
lim f 1x2 q, but
xS4
lim f 1x2 q, so lim f 1x2
xS4 xS4
does not exist.
7. f 1x2 is discontinuous at
lim but lim f 1x2 3.
xS2 xS2
8.
4
a. 1 d.
5
3
b. 6 e.
1
12
c.
1
1 f.
9
2
9. a. 6x 1
b. 1 x 2
10. a. 3x 2 8x 5
b.
3x 2
2x 3 1
c.
6
1x 32 2
d. 4x1x 2 3214x 5 5x 12
1x 2 32 2 120x 4 52
14x 2 12 4 184x 2 80x 92
e.
13x 22 4
f. 53x 2 12x 12 3 4 4
32x 612x 12 2 4
11.
12.
4x 3y 10 0
3
13. a. p¿1t2 4t 6
b. 46 people per year
c. 2006
14. a. f ¿1x2 5x 4 15x 2 1;
f –1x2 20x 3 30x
b. f ¿1x2 4 f –1x2 12
x 3; x 4
c. f ¿1x2 2 f –1x2 3
x 3; x 5
d. f ¿1x2 4x 3 4 x 5;
f –1x2 12x 2 20
x 6
15. a. maximum: 82, minimum: 6
b. maximum: 9 1 minimum: 2
3 ,
e 1
c. maximum: , minimum:
1 e 4 2
d. maximum: 5, minimum: 1
16. a. v1t2 9t 2 81t 162,
a1t2 18t 81
b. stationary when t 6 or t 3,
advancing when v1t2 7 0, and
retreating when v1t2 6 0
c. t 4.5
d. 0 t 6 4.5
e. 4.5 6 t 8
17.
18.
14 062.5 m 2
r 4.3 cm, h 8.6 cm
19. r 6.8 cm, h 27.5 cm
20. a. 140 2x
b. 101 629.5 cm 3 ; 46.7 cm by 46.7 cm
by 46.6 cm
21.
22.
x 4
$70 or $80
23. $1140
dy
24. a. 10x 20,
dx
x 2 is critical number,
Increase: x 6 2,
Decrease: x 7 2
dy
b.
c.
12x 16,
dx
x 4 is critical number,
3
Increase: x 7 4 3 ,
Decrease: x 6 4 3
dy
dx 6x2 24,
x ;2 are critical numbers,
Increase: x 6 2, x 7 2,
Decrease: 2 6 x 6 2
dy
d. The function has
dx 2
1x 22 2 .
no critical numbers. The function is
decreasing everywhere it is defined,
that is, x 2.
25. a. y 0 is a horizontal asymptote.
x ;3 are the vertical asymptotes.
There is no oblique asymptote.
Q0, 8 is a local maximum.
9 R
b. There are no horizontal asymptotes.
x ;1 are the vertical asymptotes.
y 4x is an oblique asymptote.
13, 632 is a local
maximum, 1 3, 632 is a local
minimum.
26. a.
y
30
20
10
–3 –2 –1
0
–10
y = 4x 3 + 6x 2 – 24x – 2
1
2
x
b.
4 6
–6 –4 –2 0
–2
2
27. a. 1202e 5x1 –4
–6
b. e 3x 13x 12
c. 13 ln 626 3x8
d. 1cos x2e sin x
28.
29.
y 2e1x 12 e
a. 5 days
b. 27
30. a. 2 cos x 15 sin 5x
b. 8 cos 2x 1sin 2x 12 3
c.
2x 3 cos 3x
2x 2 sin 3x
d.
1 2 cos x
1cos x 22 2
e.
f.
31. about 4.8 m
32. about 8.5 m
Chapter 6
2x sec 2 x 2 2 tan x sec 2 x
2x sin x 2 cos 1cos x 2 2
Review of Prerequisite Skills,
p. 273
3
3
1. a. d.
2
2
2
b. 3 e.
2
1
c. f. 1
2
——–—–
3x
y =
x 2 – 4
2.
3.
4
3
a. AB 29.7, B 36.5° ,
C 53.5°
b. A 97.9° , B 29.7° ,
C 52.4°
4. Z 50° , XZ 7.36,
YZ 6.78
5. R 44° , S 102° , T 34°
9. 59.4 cm 2
6. 5.82 km
7. 8.66 km
8. 21.1 km
6
4
2
y
x
NEL
Answers 659