Math 70 Final Exam Review
probe
Name___________________________________
M U L T IPLE C H O I C E. C hoose the one alternative that best completes the statement or answers the question.
Perform the indicated operation.
1) (- 5x + 6y)(- 4x - 3y + 1)
A) 20x 2 - 9xy - 5x - 18y 2 + 6y
1)
B) 20x 2 - 24xy - 5x - 18y2 + 6y
D) 20x 2 + 15xy - 5x - 18y2
C) 20x 2 - 9xy - 9y 2
Factor completely. State that the polynomial is prime i f it cannot be factored.
2) 9x 2 + 34x - 8
A) (9x - 10)(9x - 2)
B) (9x - 2)(x + 4)
C) (2 - 9x)(9x - 2)
3) 60x 2 + 35xy + 5y 2
A) prime
C) 5(3x + y)(4x + y)
2)
D) (9x - 2)(x - 4)
3)
B) (15x + 5y)(4x + y)
D) 5(3x - y)(4x - y)
4) 72a 4 - 50b2
A) 2(6a 2 + 5b)(6a 2 - 5b)
4)
B) 2(6a 2 + 5b)2
D) 2(6a 2 - 5b)2
C) prime
1
Perform the in dicated operation and si mpl ify.
k2 + 6k + 9
k 2 + 7k
·
5)
k 2 + 10k + 21 k2 + 8k + 15
A)
k
k+5
B)
5)
k 2 + 7k
k+5
C)
k
2
k + 10k + 21
D)
1
k+5
Perform the indicated operations and sim pl i fy.
x
3
6)
2
2
x - 16 x + 5x + 4
6)
A)
x 2 - 2x + 12
(x - 4)(x + 4)(x + 1)
B)
x 2 - 2x + 12
(x - 4)(x + 4)
C)
x 2 + 2x + 12
(x - 4)(x + 4)(x + 1)
D)
x2 - 2
(x - 4)(x + 4)(x + 1)
Solve the equation.
3
1 3
z - 2z + =
7)
10
5 5
A) 4
7)
B) -
4
17
C) -
2
2
17
D) -
8
17
Solve the equation. I f the solutions involve square roots, give both the exact solutions and the approximate solutions to
three deci mal p laces.
8) 2k 2 - 11k - 6 = 0
8)
B) -
A) - 2, 6
9) 2n 2 = - 10n - 1
- 5 + 23
A)
4
C)
10)
- 10 + 23
2
1
,2
2
C) -
1
,6
2
D)
1
1
,11
2
9)
- 0.051,
- 5 - 23
4
- 2.602,
- 10 - 23
2
- 2.449
- 7.398
B)
-5 + 3
2
D)
- 5 + 23
2
- 1.634,
-5 - 3
2
- 0.102,
- 5 - 23
2
7
6
- 42
=
m + 3 m - 3 m2 - 9
A) 3
- 3.366
- 4.898
10)
B) N o solution
C) - 3
3
D) 7
Solve the i nequal ity and graph the sol ution.
11) 9 + 7t - 8 6t - 2
11)
A) [ - 3, )
B) (- , 7)
C) (- , - 3]
D) (7, )
Sol ve the q uadratic i neq ual ity. G rap h the sol ution.
12) v2 + 11v + 28 0
12)
A) [- 4, )
B) (- , - 7]
C) (- , - 7]
D) [- 7, - 4]
[- 4, )
Sol ve the i neq ual ity.
x + 29
<9
13)
x+3
A) - ,
1
4
13)
3,
B)
1
,3
4
C) - , - 3
4
1
,
4
D) - 3,
1
4
Sim pl i fy the expression. I f the expression contains any variables, assume that they represent positi ve real n umbers. Write
your answ er w ith onl y positive exponents.
-2
x - 3 y4
14)
14)
y-5
A)
1
6
x y18
B)
x6
y 18
C)
y 18
x6
D)
x6
y 13
Evaluate the expression.
125 - 2/3
15)
8
A)
4
25
15)
B) -
25
4
C)
25
4
D)
4
125
Factor the expression.
1/2
- 1/2
+ 4(x 2 - 2) (5x + 5)
16) x(5x + 5)2 (x 2 - 2)
- 1/2 2
(4x + x - 8)
A) (5x + 5)2 (x 2 - 2)
- 1/2 2
2
(4x + 5x - 3)
C) (5x + 5)(x - 2)
16)
- 1/2
(9x 2 + 5x - 8)
B) (5x + 5)(x 2 - 2)
1/2
D) (5x + 5)(x 2 - 2) (9x 2 + 5x - 8)
Si m p l i f y. A ssume that al l variab les represent positi ve real n um bers.
17) 20k7 q8
A) (2q4 ) 5k 7
B) (2k 3 q4) 5
C) (2k 3 q4) 5k
5
17)
D) (2k 7 q8) 5k
Sim pl i fy the expression b y remov ing as many factors as possible from u nder the radical. A ssume that al l variables
represent positive real numbers.
5
18) s · s
18)
10
7
5
7
s7
A)
B) 2s
C) s2
D) s2
Perform the indicated operations and simp l i fy. A ssume al l variables represent positive real numbers.
19) 3 18 - 6 98 - 2 128
A) - 173 2
B) 3 2
C) - 49 2
D) 173 2
Rational ize the denominator. A ssu me that al l radicands represent positive real nu mbers.
3
20)
x-2
A)
3 x-6
x+4
B)
9
x+4
C)
9
x-4
D)
20)
3 x+6
x-4
Find the slope of the line passing through the given pair of points.
21) (4, - 5) and (5, - 10)
1
A) B) 5
C) - 5
5
5
D) 3
Find an eq uation in slope - intercept form (w here possib le) for the li ne.
22) T hrough (- 5, 8) and (3, - 9)
17
21
13
23
17
21
xxxA) y = B) y = C) y =
8
8
12
4
8
8
13
23
xD) y =
12
4
6
19)
21)
22)
23) T hrough (5, 7), parallel to - 9x + 7y = - 31
5
31
7
7
A) y = - x B) y = x 7
7
9
9
9
4
C) y = x +
7
7
9
4
D) y = - x 7
7
23)
24) T hrough (- 2, - 8), perpendicular to - 8x - 3y = 40
3
8
A) y = x
B) y = x - 58
8
3
3
29
C) y = - x +
8
4
3
29
D) y = x 8
4
24)
Sol ve the prob lem.
25) In a lab experiment 14 grams of acid were prod uced in 16 minutes and 19 grams in 23 minutes. Let
y be the grams produced in x minutes. W rite a linear equation for grams prod uced.
5
18
7
18
5
18
5
18
A) y = x B) y = x C) y = - x D) y = x +
7
7
5
7
7
7
7
7
G ive the domain of the function.
26) f(x) = 6 - x
A) [0, 6]
25)
26)
B) (- , )
C) (- , 6)
7
(6, )
D) (- , 6]
Evaluate the function.
27) f(x) = 3x 2 + 2x - 5; Find f(t - 1).
A) - 4t2 + 3t - 4
B) 3t2 - 4t - 4
27)
C) 3t2 - 4t + 0
G raph the parabola and give its vertex, axis, x -intercepts, and y -i ntercepts.
28) f(x) = - x 2 - 6x - 8
A) vertex (3, 1); axis is x = 3;
x - intercepts are 2 and 4; y - intercept is - 8
B) vertex (- 3, - 1); axis is x = - 3;
x - intercepts are - 2 and - 4; y - intercept is 8
8
D) 3t2 - 13t + 0
28)
C) vertex (- 3, 1); axis is x = - 3;
x - intercepts are - 2 and - 4; y - intercept is - 8
D) vertex (3, - 1); axis is x = 3;
x - intercepts are 2 and 4; y - intercept is 8
Sol ve the prob lem.
29) If an object is throw n up w ard w ith an initial velocity of 14 feet per second, then its height is given
by
h = - 14t2 + 112t. W hat is its maximu m height?
A) 336 ft
B) 168 ft
C) 224 ft
9
D) 112 ft
29)
Find the asymptotes of the function.
- 1x + 5
30) y =
18 - 6x
30)
A) Vertical asy mptote at x = 3; horizontal asymptote at y = 1
1
B) Vertical asy mptote at x = 3; horizontal asymptote at y =
6
C) Vertical asy mptote at x = 3; horizontal asymptote at y = D) Vertical asy mptote at x = -
31) y =
1
6
1
; horizontal asymptote at y = 3
6
x 2 - 49
x-7
A)
B)
C)
D)
31)
Vertical asy mptote at x = 7; no horizontal asymptote
N o asymptotes; hole at x = 7
N o vertical asymptote; horizontal asymptote at y = 7
Vertical asy mptote at x = - 7; no horizontal asymptote
Solve the equation.
32) 3 (6 + 3x) =
A)
1
27
1
9
32)
B) - 3
C) 9
D) 3
Write the exponential equation i n logarithmic form.
1
33) 2 - 2 =
4
1
A) log2 - 2 =
4
33)
1
B) log2 = - 2
4
Write the logarithmic equation i n exponential form.
34) ln x = 9
A) ex = 9
B) 9 e = x
C) log1/4 2 = - 2
1
D) log - 2 = 2
4
C) x 9 = e
D) e9 = x
34)
10
Evaluate the logarithm w ithout using a calculator.
1
35) log7
343
A) - 49
35)
B) - 3
C) 49
D) 3
Rewrite the expression as a sum, di f ference, or product of sim pler logarithms.
5
6 2
36) log7
3
10
log 76 +
A)
1
log 7 2
5
B)
1
log 7 10
3
C) log7 6 +
1
1
log7 2 - log7 10
5
3
36)
log 76 + 5log 72
3log7 10
D) log7 6 + 5log7 2 - 3log7 10
Solve the equation.
37) log (2 + x) - log (x - 3) = log 2
A) - 8
37)
3
C)
2
B) 8
D) N o solution
Solve the equation. Round decimal answers to the nearest thousandth.
38) 6e2x - 1 = 36
A) 18.500
B) 0.799
C) 1.396
11
38)
D) 0.396
Fi n d the domai n of the f u nction.
39) f(x) = log 4 (25 - x 2)
A) - 5 < x < 5
39)
B) - 5 x 5
C) - 25 < x < 25
D) x < - 5 and x > 5
D eci de w hether the l i m it exists. I f it exists, f i nd its val ue.
40) lim f(x)
x 1
A) 0
40)
B) Does not exist
C) - 1
D) 1
Use the properties of l imits to help decide w hether the l imit exists. I f the l imit exists, f in d its value.
x 2 + 15x + 56
41) lim
x+7
x -7
A) Does not exist
42) lim
x 0
A)
B) 210
C) 1
D) 15
1
1
x+6 6
42)
x
1
36
41)
B) -
1
36
C) Does not exist
12
D) 0
x-3
x-9
43) lim
x 9
A)
44) lim
x
1
6
43)
B) 3
C) 0
D)
1
3
5x 2 + 6x - 3
- 4x 2 + 5
A) -
5
4
44)
B) 0
D) -
C)
5
3
6x 5 - x + 4
45) lim
x
9x 2 - x - 6
A) Does not exist
45)
B)
C)
2
3
D)
Use the properties of l im its to help decide w hether each l imit exits. I f a l im it exists, f ind its value.
46) Let f(x) = - 2x + 3 if x 1 . Find lim f(x).
- 7x + 8 if x > 1
x 1
A) 1
B) 8
C) Does not exist
D) 3
Sol ve the prob lem.
47) The blood alcohol level h hours after consumption of 2 ounces of pure ethanol is given by
0.55h
C(h) =
. Find the blood alcohol level as h approaches infinity.
h3 - h2 + 5
A) .11
B) .55
C)
13
46)
D) 0
47)
Find al l values x = a w here the f u nction is d isconti n uous.
x-8
48) f(x) = ln
x+3
A) N o w here
48)
B) a = - 3
C) a = 8, - 3
Find the value of the constant k that makes the function continuous.
2
49) g(x) = x - 7 if x < 6
5kx
if x 6
29
6
A) k =
B) k = 29
C) k =
30
5
D) a = - 8, 3
49)
D) k = 13
Find the average rate of change for the function over the given interval.
3
betw een x = 4 and x = 7
50) y =
x-2
A) 2
B)
1
3
C) -
3
10
50)
D) 7
Find the instantaneous rate of change using the l imit def inition for the function at the given value.
51) s(t) = 3t2 + 5t - 7 at t = - 2
A) - 1
B) 1
C) - 17
14
D) - 7
51)
Find f'(x) at the given value of x using the l i mit def in ition.
52) f(x) = 10x 2 + 8x; Find f (9).
A) 188
B) 220
52)
C) - 243
D) 252
Find the equation of the tangent l ine to the curve w hen x has the given value.
7
;x=4
53) f(x) =
x+1
A) y =
7
7
x+
25
25
54) f(x) = x 2 - x ; x = - 4
A) y = - 9x - 16
B) y = -
14
63
x+
25
25
C) y = -
7
7
x+
25
25
B) y = - 9x + 12
C) y = - 9x + 16
7
63
x+
25
25
D) y = - 9x - 12
55)
2
4
12
3/2
2
x
x
x2
C) - 2 x +
D) y = -
54)
Fi nd the deri vative.
4
4
4
, find f'(x)
- +
55) f(x) =
x x x3
A) -
53)
B)
4
12
2
x
x2
2
4
12
1/2
2
x
x
x4
D) -
15
2
4
12
+
3/2
2
x
x
x4
Find an equation for the l ine tangent to gi ven curve at the given value of x.
56) y = x 3 - 16x + 3; x = 4
A) y = 3
B) y = 32x - 125
C) y = 35x - 125
56)
D) y = 32x + 3
Sol ve the prob lem.
57) Exposure to ionizing radiation is know n to increase the incidence of cancer. O ne thousand
laboratory rats are exposed to identical doses of ionizing radiation, and the incidence of cancer is
recorded during subsequent days. The researchers find that the total number of rats that have
developed cancer t months after the initial exposure is modeled by N (t) = 1.04t2.3 for 0 t 10
57)
months. Find the rate of growth of the number of cancer cases at the 7th month. Round your
answer to the nearest tenth, if necessary.
A) 25 cases/month
B) 34 cases/month
C) 210.1 cases/month
D) 30 cases/month
Use the prod uct rule to f i n d the deri vative.
58) f(x) = (6 x - 2)(5 x + 7)
A) f'(x) = 30x + 16x 1/2
58)
B) f'(x) = 30x + 32x 1/2
D) f'(x) = 30 + 32x - 1/2
C) f'(x) = 30 + 16x - 1/2
16
Use the q uotient rule to f i nd the deri vative.
x 2 - 3x + 2
59) y =
x7 - 2
59)
A)
dy
- 5x 8 + 18x 7 - 13x 6 - 4x + 6
=
dx
(x 7 - 2)2
B)
dy
- 5x 8 + 19x 7 - 14x 6 - 4x + 6
=
dx
(x 7 - 2)2
C)
dy
- 5x 8 + 18x 7 - 14x 6 - 3x + 6
=
dx
(x 7 - 2)2
D)
dy
- 5x 8 + 18x 7 - 14x 6 - 4x + 6
=
dx
(x 7 - 2)2
Write an eq uation of the tangent line to the graph of y = f(x) at the point on the graph w here x has the indicated val ue.
- 5x 2 + 10
,x=0
60) f(x) =
60)
- 3x - 2
A) y = -
15
x-5
2
B) y =
15
x+5
2
C) y =
15
x-5
2
D) y = -
15
x+5
2
Fi nd the deri vative.
61) y = (2x - 1)3 (x + 7) - 3
dy
= 45(2x - 1)3 (x + 7) - 2
A)
dx
C)
61)
dy
= 45(2x - 1)2 (x + 7) - 4
B)
dx
dy
= 45(2x - 1)2 (x + 7) - 3
dx
D)
17
dy
= 45(2x - 1)3 (x + 7) - 4
dx
62) f(x) = (x 3 - 8)2/3
A) f'(x) =
x2
3
x3 - 8
62)
B) f'(x) =
2x
3
C) f'(x) =
x3 - 8
x
3
D) f'(x) =
x3 - 8
2x 2
3
x3 - 8
Find the equation of the tangent l ine to the graph of the given function at the given val ue of x.
63) f(x) = x 3 x 3 + 3; x = 1
35
20
x+
A) y =
6
3
27
13
xB) y =
4
4
27
19
xC) y =
4
4
35
20
xD) y =
6
3
B) 10ex3x (3x + 2)
C) 5xe3x (3x + 2)
D) 5xe3x (2x + 3)
B) 63 (ln 9) 9 7x
C) 63 (ln 7) 9 7x
D) 9 (ln 7) 97x
Fi nd the deri vative.
64) y = 5x 2 e3x
A) 10xe3x (2x + 3)
64)
65) y = 9 7x
A) 7 (ln 9) 97x
63)
65)
18
Find the derivative of the function.
66) y = ln (4 + x 2 )
2
A)
x
67) y = log (5x - 7)
1
A)
ln 10 (5x - 7)
66)
8
B)
x
2x
C)
2
x +4
1
D)
2x + 4
67)
B)
5
ln 10
C)
5
ln 10 (5x - 7)
D)
5x - 7
5 ln 10
Find al l the critical numbers of the function.
68) f(x) = 4x 3 + 12x 2 - 96x + 8
A) - 2
68)
B) 12
C) 4, - 2
D) - 4, 2
69) f(x) = (x + 5)2/5
A) 5
69)
B) 2
C)
25
2
D) - 5
Find the open interval(s) w here the function is changing as requested.
70) Increasing; y = x 4 - 18x 2 + 81
A) (- , 0)
B) (- 3, 0), (3, )
C) (- 3, 0)
19
70)
D) (- 3, 3)
71) Decreasing;
2
A) 0,
7
y = x 2/5 + x 7/5
71)
B)
2
,7
C)
2
,, (0, )
7
2
D) ( , 0), ,
7
Find the x - val ue of al l points w here the function has relative extrema. Fi nd the value(s) of any relative extrema.
72) f(x) = x 3 - 12x + 2
72)
A)
B)
C)
D)
73) f(x) =
A)
B)
C)
D)
Relative maximum of 18 at - 2; Relative minim um of - 14 at 2.
Relative minim um of - 13 at 3.
Relative maximum of 1 at 0; Relative minimum of - 3 at 2.
Relative maximum of 14 at - 2; Relative minimum of 0 at 2.
x2 + 1
x2
73)
Relative maximum of 50 at 0.
N o relative extrema.
Relative minimum of 0 at 10.
Relative maximu m of 50 at 0 ; Relative minimum of 0 at 10.
20
74) f(x) = x ln x , x > 0
1 1
A) , , relative maximum
e e
C)
74)
1
1
, relative maximum
B) - , e
e
1
1
,, relative minimu m
e
e
D) -
1 1
, , relative minimu m
e e
Find the indicated derivative of the function.
75) f(4)(x) of f(x) = 2x 6 - 7x 4 + 7x 2
A) 480x 2 - 84x
75)
B) 720x 2 - 168
C) 720x 2 - 168x
D) 480x 2 - 84
Find the largest open intervals w here the f unction is concave up ward.
76) f(x) = 4x 3 - 45x 2 + 150x
15
,
A) 4
15
B) - ,
4
15
C) - , 4
21
76)
15
,
D)
4
77) f(x) =
x
2
x +1
A) ( 3, )
77)
B) N one
C) (- , - 1), (- 1, )
D) (- , - 1)
Find the ind icated absolute extremum as wel l as al l values of x w here it occurs on the speci f ied domain.
1
78) f(x) = x 3 - 2x 2 + 3x - 4; [ - 2, 5]
3
M inimum
10
at x = 2
A) 3
79) f(x) =
B) -
8
at x = 1
3
C) -
62
at x = - 2
3
x+3
; [- 4, 4]
x-3
78)
D) - 4 at x = 0
79)
M aximum
1
A) at x = - 4
7
B) 7 at x = 4
C) N o absolute maximum
D) - 1 at x = 0
22
Fi nd the absolute extrema i f they exist as wel l as w here they occur.
80) f(x) = - 3x 4 + 16x 3 - 18x 2 + 9
A)
B)
C)
D)
80)
N o absolute extrema
A bsolute maximu m of 4 at x = 1; no absolute minima
A bsolute maximu m of 17 at x = 2; no absolute minima
A bsolute maximu m of 36 at x = 3; no absolute minima
Sol ve the prob lem.
81) Find t wo numbers x and y such that their sum is 420 and x 2 y is maximized.
A) x = 105, y = 315
B) x = 140, y = 280
C) x = 280, y = 140
23
81)
D) x = 315, y = 105
82) Supertankers off - load oil at a docking facility shore point 3 miles offshore. The nearest refinery is
10 miles east of the docking facility. A pipeline must be constructed connecting the docking facility
w ith the refinery. T he pipeline costs $300,000 per mile if constructed under water an d $200,000 per
mile if over lan d.
3 mi
10 mi
Locate point B to minimize the cost of construction.
A) Point B is 9.15 miles from Point A .
C) Point B is 5.06 miles from Point A .
24
B) Point B is 2.68 miles from Point A .
D) Point B is 5.67 miles from Point A .
82)
83) From a thin piece of cardboard 10 in. by 10 in., square corners are cut out so that the sides can be
fol ded up to make a box. W hat d imensions w ill yield a box of maximum volume? W hat is the
maxim um volu me? Round to the nearest tenth, if necessary.
A) 3.3 in. by 3.3 in. by 3.3 in.; 37 in.3
B) 6.7 in. by 6.7 in. by 3.3 in.; 148.1 in.3
C) 5 in. by 5 in. by 2.5 in.; 62.5 in.3
D) 6.7 in. by 6.7 in. by 1.7 in.; 74.1 in.3
Find dy/dx by impl icit di f ferentiation.
84) x 3 + 3x 2 y + y 3 = 8
x 2 + 3xy
A) x2 + y2
84)
x 2 + 2xy
B) x2 + y2
x 2 + 2xy
C)
x2 + y2
85) y5 e x + x = y 3 x
x 2 + 3xy
D)
x2 + y2
85)
dy
y3 - 1
=
A)
dx 5y 4 ex - 3x y2
C)
83)
dy
y3 - 1
=
B)
dx 5y 4 ex - 3x y2 + 1
dy y 3 - y 5 ex - 1
=
dx 5y 4 ex - 3x y2
D)
25
dy
y 3 - y5 e x - 1
=
dx 5y 4 ex - 3x y2 - 1
Find the equation of the tangent l ine at the given point on the curve.
86) 2xy - 2x + y = - 14; (2, - 2)
5
22
5
22
6
22
A) y = - x +
B) y = x C) y = - x +
6
6
6
6
5
5
86)
6
22
D) y = x 5
5
A ssume x and y are functions of t. E valuate dy/dt.
x+y
= x 2 + y 2 ; dx/dt = 12, x = 1, y = 0
87)
x-y
A)
1
12
B) -
87)
1
12
C) 12
D) - 12
Sol ve the prob lem.
88) A container, in the shape of an inverted right circular cone, has a radius of 8 inches at the top and a
height of 10 inches. A t the instant w hen the water in the container is 9 inches deep, the surface level
is falling at the rate of - 2 in./s. Find the rate at w hich w ater is being drained.
A) - 311.04 in.3 /s
B) - 286.5 in.3 /s
C) - 456 in.3 /s
D) - 325.71 in.3 /s
26
88)
89) A man 6 ft tall w alks at a rate of 5 ft/s a w ay from a lamppost that is 16 ft high. A t w hat rate is the
length of his shadow changing w hen he is 30 ft away from the lamppost?
15
15
ft/s
ft/s
A) 25 ft/s
B)
C)
D) 3 ft/s
11
22
Find the integral.
27
dx
90)
x2
90)
A) - 27x + C
91)
( x+
A)
3
B) 27x + C
C)
27
+C
x
D) -
27
+C
x
91)
x) dx
1 3/2 2 4/3
x
+ x
+C
2
3
C) 2 x + 2
92)
89)
3
B) 2 x + 3
x+C
D)
3
x+C
2 3/2 3 4/3
x
+ x
+C
3
4
8e4y dy
A) 2e4y + C
92)
B)
1 4y
e +C
2
C)
27
1 4y
e +C
4
D) 4e4y + C
93)
2 3x dx
A)
94)
93)
2 3x
+C
3 ln 2
B)
2 3x
+C
ln 2
C)
2 4x
+C
4
D)
2 3x
+C
3
x 6
dx
+
6 x
94)
A) x + C
C)
B) x ln 6 + 6 ln x + C
1 2
x + 6 ln x + C
12
D)
1
x+C
6
Sol ve the prob lem.
95) Suppose that an object's acceleration function is gi ven by a(t) = 4t + 10. The object's initial velocity,
v(0), is 3, and the object's initial position, s(0), is 12. Find s(t).
4
2
A) s(t) = t3 + 5t2 + 12t + 3
B) s(t) = t3 + 5t2 + 3t + 12
3
3
C) s(t) =
2 3
t + 5t2 + 3t
3
D) s(t) = 2t2 + 10t + 3
28
95)
96) T he number of mosquitoes in a lake area after an insecticide spraying decreases at a rate of
M (t) = - 7000e - 0.5t mosquitoes per hour. If there were 14,000 mosquitoes initiall y, how many w ill
there be after 5 hours?
A) M (5) 1149 mosquitoes
B) M (5) 14,000 mosquitoes
C) M (5) 2,077,784 mosquitoes
D) M (5) 170,555 mosquitoes
Find the integral.
dr
97)
6r - 7
A)
98)
9z
A)
1
4
6r - 7 + C
96)
97)
B)
1
6
6r - 7 + C
C)
1
2
6r - 7 + C
3z 2 - 7 d z
D)
1
3
6r - 7 + C
98)
1
(3z 2 - 7)3/2 + C
2
B) (3z 2 - 7)3/2 + C
C) z(3z 2 - 7)3/2 + C
D)
29
1
z(3z 2 - 7)3/2 + C
2
99)
x
5
(7x 2 + 3)
A)
C)
100)
dx
99)
-1
4
56(7x 2 + 3)
-7
6
3(7x 2 + 3)
+C
B)
+C
D)
6
14(7x 2 + 3)
-7
4
3(7x 2 + 3)
+C
+C
2
(1 - 6x)e3x - 9x dx
A)
100)
1
2
(1 - 6x)e3x - 9x + C
3
B)
2
C) 3e3x - 9x + C
101)
-1
t2 + 2
t3 + 6t + 2
2
D) 3(1 - 6x)e3x - 9x + C
dt
101)
A) 3 ln t3 + 6t + 2 + C
C) -
1 3x - 9x 2
e
+C
3
1
2
3(t3 + 6t + 2)
B)
+C
ln t3 + 6t + 2
+C
3
D) -
30
3
2
(t3 + 6t + 2)
+C
102)
(ln x)75
dx
x
A)
(ln x)76
+C
76
102)
B)
(ln x)76
+C
x
C)
(ln x)76
+C
76x
D) 75(ln x)74 + C
A pproximate the area un der the graph of f(x) and above the x -axis usi ng n rectangles.
8
103) f(x) = from x = 2 to x = 6; n = 4; use right endpoints
x
A) 10.27
B) 7.60
C) 10.67
103)
D) 8.72
Provi de the proper response.
104) If f(b) = 4 and f(x) is decreasing on the interval [a, b], then w hich method of estimating the area
under the graph of f(x) and above the x - axis w ill yield the lowest value? A ssume that n = 10 in all
cases.
A) Using right endpoints
B) Using midpoints
C) Using left endpoints
D) Cannot be determined
Evaluate the defin ite integral.
6
(3x 2 + x + 5) dx
105)
0
A) 518
104)
105)
B) 119
C) 47
31
D) 264
4
106)
(x 3/2 + x 1/2 - x - 1/2) dx
106)
1
A) 46
e
107)
1
8x -
B)
1
0
C)
226
15
D)
224
15
11
dx
x
A) 4e2 - 4
108)
44
3
10r
9 + 5r2
A) 2 14 - 6
107)
B) 8e2 - 11
C) 4e2 - 15
D) 4e2 - 11
dr
108)
B) - 2 14 + 6
C)
32
14
3
2
2
D)
14 - 3
Use the definite integral to find the area between the x -axis and f(x) over the indicated i nterval.
3
; [1, 3]
109) f(x) =
x3
A)
4
3
110) f(x) = - x 2 + 9; [0, 5]
98
A)
3
B)
1
3
C)
1
2
D) 3
110)
10
B)
3
10
C)
9
5
D)
9
Fi nd the area of the shaded region.
111)
111)
y=
A)
16
3
109)
B)
x-3
22
3
C)
33
29
3
D)
38
3
Sol ve the prob lem.
112) T he rate of change in a person's body tem perature, w ith respect to the dosage of x milligrams of a
5
drug, is given by D'(x) =
. O ne milligram raises the temperature 2.4°C. Find the function
x+8
112)
giving the total temperature change.
B) D(x) = ln
A) D(x) = 5 ln x + 8 + 2.4
C) D(x) = ln
5
x+8
- 8.6
5
x+8
- 2.4
D) D(x) = 5 ln x + 8 - 8.6
113) For a certain drug, the rate of reaction in appropriate units is given by R'(t) =
7
3
+ , where t is
t t2
113)
measured in hours after the drug is administered. Find the total reaction to the drug from t = 2 to t
= 9. Round to two decimal places, if necessary.
A) 11.7
B) 9.2
C) 22.57
D) 18.4
114) T he number of cows that can graze on a ranch is approximated by C(x,y) = 9x + 5y - 8, w here x is
the number of acres of grass and y the n umber of acres of alfalfa. If the ranch has 75 acres of alfalfa
and 90 acres of grass, how man y cows may graze?
A) 1125 cows
B) 1117 cows
C) 1177 cows
D) 1185 cows
34
114)
Fi nd the partial derivative.
2xy3
.
115) Fin d f y (- 1, 2) w hen f(x, y) =
x2 + y2
A)
184
25
B) -
56
25
116) Let z = g(x,y) = 2x + 6x 2 y 2 - 7y 2 . Find
A) 12yx - 14y
115)
C) -
56
5
D)
48
25
z
.
y
116)
B) 2 + 12yx 2
C) 12yx - 12y
D) 12yx 2 - 14y
Fin d f x (x, y).
117) f(x, y) = y ln (4x + 9y)
117)
A) fx (x, y) = y ln (4x + 9y)
4y
B) fx (x, y) =
4x + 9y
4xy
C) fx (x, y) =
4x + 9y
4
D) fx (x, y) = ln (4x + 9y) +
4x + 9y
118) f(x, y) = xye - x
A) y(e - x - x)
118)
B) - ye - x
C) e - x (1 - x)
35
D) ye - x (1 - x)
Find val ues of x and y such that both f x (x, y) = 0 and f y (x, y) = 0.
119) f(x,y) = x 3 - 4xy + 8y
4
A) x = , y = 2
3
119)
B) x = 2, y = 2
C) x = 0, y = 0
D) x = 2, y = 3
Sol ve the prob lem.
120) T he intelligence quotient in psychology is given by Q(m, c) = 100
m
, w here m is an individual's
c
mental age and c is the individual's chronological, or actual, age. Find
A)
100m
c
C) -
B) 100m
36
100m
c
Q
.
c
D) -
100m
c2
120)
Answer Key
Testname: MATH 70 FINAL EXAM REVIEW
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
12)
13)
14)
15)
16)
17)
18)
19)
20)
21)
22)
23)
24)
25)
26)
27)
28)
29)
30)
31)
32)
33)
34)
35)
36)
37)
38)
39)
40)
41)
42)
43)
44)
45)
46)
47)
48)
49)
50)
A
B
C
A
A
A
B
C
D
B
A
B
C
B
A
B
C
A
C
D
C
A
C
D
D
D
B
C
C
B
B
B
B
D
B
C
B
C
A
D
C
B
A
A
B
A
D
C
A
C
51)
52)
53)
54)
55)
56)
57)
58)
59)
60)
61)
62)
63)
64)
65)
66)
67)
68)
69)
70)
71)
72)
73)
74)
75)
76)
77)
78)
79)
80)
81)
82)
83)
84)
85)
86)
87)
88)
89)
90)
91)
92)
93)
94)
95)
96)
97)
98)
99)
100)
D
A
D
A
D
B
D
C
D
C
B
D
C
C
A
C
C
D
D
B
B
A
B
C
B
D
A
C
C
D
C
B
D
B
C
D
C
D
D
D
D
A
A
C
B
A
D
B
A
B
101)
102)
103)
104)
105)
106)
107)
108)
109)
110)
111)
112)
113)
114)
115)
116)
117)
118)
119)
120)
37
B
A
B
A
D
C
C
A
A
B
D
D
A
C
B
D
B
D
D
D