Download Fall Final Answers

Fall Final Answers
Chapter 2:
1. a. About 3.25
b. undefined c. -1 d. 3
e. does not exist
f. 2
h. 
i. does not exist
j. -2
k. 
l. 0
m. x = -3 removable, x = -1 non-removable, x = 0 removable, x = 2 non-removable
n. because lim f(x)  lim f(x)
x2
2. D
g. 
x2
3. A
4. B
5. E
5. f(c) is defined, lim f(x) exists, lim f(x) = f(c)
xc
6. A
9. a. 1
xc
7. x = -2
b. 3
8. a. DNE
b. 75
c. DNE b/c lim f(x)  lim f(x)
x2
lim f(x) does not exist
c. 6
D. 
d. f(2) = 1 ; Not continuous because
x2
x2
10. D
11. D
Chapter 3:
1. 2x + 2
4.
8
x
2. 5
4  3y
3x  2y
5. y  
3
8. a. 3x2 – 6x
b.
2x 3  2
x
3
3. B
6. 48(2x + 3)2
c.
2
(x  1)
7. E
d.
2
4
4
9x
e.
3
f. 12x3 – 18x2 + 32x – 14
1

g. 5 x 2  
x

i. 2sin(2x) – 4cos(x)sin(x)
j.  3 csc(3x) cot(3x)  3 csc2 (3x)
l. 5cot x ( csc2 x) ln(5)
m.  2x csc2 (sin(x2 ) cos(x2 ))
o.
3x 4
 2x ln(x3  1)
x3  1
r.
1 3x
(e  e  3x ) 1 / 2 (3e3x  3e  3x )
2
9.
d2 y
dx
2

1 
 2x 

x2 

p. 1 + 2tan(x)
1
 1
 2y 3 (6  2x) 2  2y 2 at  3,  =
8
 4
2x
3 (x 2  1) 2
3
h. -9sin(3x + 1)
n. y' 
k.
5  2xy3
1
3x
3x2 y 2  3
q. exe-1
tan 3
sec 2 3
s. e
10. m = 2/5
t.
k = 8/5
3x 2 e x  2  x 3 e x  2
(e x  2 ) 2
11. A
12. C
13. C
17. dV/dt = 0.1(SA)
14. A
15. C
16. dA/dt = -7.5cm2/sec
18. C
Chapter 4
1. D
2. a. -1, 1 (Hole at 0) b. x = 2, x = -2
5. C
6. B
c. y = 1
3. 31,250
4.  7 , 7 


2
2
7. B
9. Yes:
10. Yes
x=a
x=m
11. Absolute Maximum = 16/3
12. a. b/c f’(x) goes from + to – at x = -1/2
b. b/c f’(-3) = 0 you have a horizontal tangent but f’(x) goes from + to + at this x – value so it is not an
extrema
c. b/c in the interval (1,  ) f(x) is increasing b/c f’(x) > 0
13. E
14. C
15. A
16. B
17. a. x = -3 neither, x = 1 relative minimum, x = 0 relative maximum
b. 3 points of inflection because f’(x) goes from increasing to decreasing or decreasing to increasing at
each of these points.
c. y – 7 = 3(x + 2)
d. Increasing (,0)  (1, ) because f’(x) > 0 ; Decreasing (0,1) because f’(x) < 0
e. These are approximate values: Concave up: (3,1.4)  (0.6, ) b/c f’(x) is increasing
Concave down: (,3)  (1.4,0.6) b/c f’(x) is decreasing
18. 123 2
19. 64 or 65 players