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AP Calculus AB Review Flashcards | StudBud
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AP Calculus AB Review
AP Calculus AB Review
25 terms
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A general review for AP Calculus AB covering various topics.
Flashcards
25 cards
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Practice quiz
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Questions
25
Answers
1
∫ (x + sin(x)) dx on the interval [0, π] =
0
π2 + 2
(1/2)π2 + 2
(1/2)π2
2
Find the integral of the following function on the range [0, 3]
3/2
0
5/2
2.5
3
Solve dx/dy = 2x/y for y
√(2x2)
4x2
2x2 + C
√(2x2 + C)
4
Find the limit as x approaches 4 of (x
2
- 16) / (x - 4)
0
8
∞
DNE
5
integral from 0 to 1 of (x
3
) / (x
4
+ 1) dx =
(1/4)ln2
(1/4)ln(2) + C
ln(2)
ln(12)
6
∫(1 / (16 + x
2
)) dx =
(1/4)sin-1(x/4) + C
(1/4)arcsin(x/4) + C
(1/4)tan-1(x/4) + C
(1/4)arctan(x/4) + C
7
CALCULATOR:
Given rate = 2100sin
2
((π/8)x) gallons/hour, find total gallons pumped after 5 hours
8400
6195
90000000
400
8
USE YOUR CALCULATOR
-185
15
-186
14
9
Find the position at t = 5 given s(0) = 4 and v(t) = 2t
19
4
29
9
10
Evaluate ∫ x
2
dx on the interval [0, 2]
6
2
8/3
3/8
11
Find the area between the curves x = 4 - y
2
and x = y - 2
12
17
20
20.833
12
∫(1/2)sec
2
(4x) dx =
(1/8)tan(4x) + C
(1/4)tan(4x)
(1/4)tan(4x) + C
4sec(4x)+C
13
Evaluate ∫( 1 / (3-x)) dx
-ln(3-x)
-ln(3-x) + C
-ln(1 / (3-x)) + C
ln(3-x) + C
14
Given F(7) and ∫(ln(12x)(x
1/2
)(e
-3x
) dx = 0 on the interval [3, 7], find F(3)
3
10
0
7
15
Find the derivative of 2
x
x2x
(2x)ln(2)
2(ln2)(2x)
x22x
16
Find the limit as x approaches -∞ of e
x
+ 1
-∞
∞
1
0
17
∫ e
6x
dx =
6e6x
e6x + C
6e6x + C
(1/6)e6x + C
18
Find the derivative of sin
-1
(5x)
cos(5x)
5sin-2(5x)
5 / √(1 - 25x2)
5 / √(1 + 25x2)
19
Equation of the line tangent to the graph of y = (2x+1) / (5x -4) at the point (1, 3) is
13x - 9y = 12
y - 3 = (-13)(x-1)
y = -13x + 10
y = (-13x) + 2
20
Given the position function s(t)=4t
3
+12t
2
+3
t
, find the velocity when acceleration = 0
0
12
36
24
21
∫( 5 / (1 + x
2
)) dx =
5arctan(x)
5arctan(x) + C
5x - 5/x + C
5tan-1(x) + C
22
limit as x approaches infinity of (3x
2
- 1) / (x
2
+ 30x)
∞
-∞
0
3
23
Find the derivative of ∫ t
3
dt when the bounds are [-2, e
x
]
e4x
e2x
ex
e3x
24
base of a solid bounded by x and y-axis and y = -2x + 4. Cross sections are squares. Area = ?
12.833
10.667
12
8
25
Given a(t) = -32t, what is the
speed
at t = 2? Given: t(0) = 10
-42
-22
22
12
