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AP Calculus AB 140418 Flashcards | StudBud
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AP Calculus AB 140418
AP Calculus AB 140418
42 terms
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AP Calculus AB Review #calculus #math #ap #derivatives #integrals
Flashcards
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Questions
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Answers
1
Choose the correct answer: ∫csc
2
(x)
dx
sin(x) + C
-cot(x) + C
sec(x) + C
-cot2(x) + C
2
The first derivative of a function provides information about the _______ of that function.
acceleration
concavity
slope
speed
3
Choose the correct answer: (d/dx)[sin(u)] =
-cos(u)·u'
cos(u)·u'
csc(u)·u'
tan(u)·u'
4
Choose the correct answer: (d/dx)[
ln(u)
] =
(1/u)∙ln(u)·u'
(1/u)·u'
ln(u)·u'
ueu·u'
5
Choose the correct answer: ∫a
x
dx
aln∣x∣ + C
ax / ln(a) + C
xln(a) + C
2x-2 + C
6
Choose the correct answer: ∫csc(x)cot(x)
dx
cot(x) + C
-csc(x) + C
-cot2(x) + C
sec(x) + C
7
The second derivative of a function provides information about the _______ of that function.
concavity
slope
acceleration
speed
8
Choose the correct answer: ∫
e
x
dx
ex + C
xex + C
xex
ex
9
For all related rates problems, you must derive each term with respect to
x
area
volume
time
10
Choose the correct answer: ∫sec(x)tan(x)
dx
sec2(x) + C
tan(x) + C
sec(x) + C
cot2(x) + C
11
Choose the correct answer.
2e(t/2) + C
e-t + C
e(t/2) + C
e(-t/2) + C
12
Choose the correct answer: (d/dx)[csc(u)] =
-csc(u)tan(u)·u'
-csc(u)cot(u)·u'
sec2(u)·u'
csc(u)cot(u)·u'
13
Choose the correct answer: (d/dx)[
vu
] =
uv' + vu'
(uv') / (vu')
u'v'
uv' - vu'
14
Choose the correct answer: (d/dx)[
u/v
] =
uv' + vu'
uv' - vu'
(vu' - uv')/(v2)
(uv') / (vu')
15
What method is used to find volume?
washer or shell method
L'Hopital's method
Pascal's method
Newton's method
16
Choose the correct answer: (d/dx)[
e
u
] =
eu + C
eu·u'
ueu·u'
ueu
17
Choose the correct answer.
32/3
16/3
14/3
28/3
18
Find the lim
x→0
(
sin
x
/ 2x)
0
1/2
-2
-1
19
Choose the correct answer: (d/dx)[cot(u)] =
sec2(u)·u'
-csc2(u)·u'
-csc(u)tan(u)·u'
sec(u)tan(u)·u'
20
Choose the correct answer: (d/dx)[tan(u)] =
sec(u)·u'
-csc2(u)·u'
sec2(u)·u'
csc(u)·u'
21
To find velocity from position, you must...
find the 1st derivative
find the 2nd derivative
integrate once
integrate twice
22
To find position from acceleration, you must...
find the 2nd derivative
integrate once
find the 1st derivative
integrate twice
23
Choose the correct answer.
8
11
14
13
24
How do you find the area between two functions of x?
top - bottom
∫(bottom - top)dx
π(top + bottom)
∫(top - bottom)dx
25
What does the mean value theorem state (for continuous, differentiable functions)?
average slope = instantaneous slope
average slope ≠ instantaneous slope
average slope > 0
Average slope < 0
26
Choose the correct answer.
6x2sin(x3)cos(x3)
6x2cos(x3)
-6x2sin(x3)cos(x3)
-6x2sin(x3)
27
Choose the correct answer: ∫sec
2
(x)
dx
sin(x)cos(x) + C
sin(x) + C
cot2(x) + C
tan(x) + C
28
Choose the correct answer.
All values of x
-3 < x < 1
x < -1 and x > 3
-1 < x < 3
29
Choose the correct answer.
-7/27
25/27
7/27
-25/27
30
Choose the correct answer.
8π/3
16π/3
32π/5
4π/3
31
Choose the correct answer: ∫(1/x)
dx
x-2 + C
x<span style="font-size: 13.3333330154419px;">n+1 + C</span>
2x-2 + C
ln∣x∣ + C
32
Choose the correct answer: (d/dx)[sec(u)] =
sec(u)tan(u)·u'
sec(u)cot(u)·u'
-csc(u)tan(u)·u'
-csc(u)cot(u)·u'
33
Choose the correct answer: (d/dx)[sec(u)] =
-csc(u)cot(u)·u'
sec(u)tan(u)·u'
-csc(u)tan(u)·u'
sec(u)cot(u)·u'
34
Choose the correct answer: (d/dx)[
a
u
] =
ln(a)·u'
au·ln(u)·u'
au·u'
au·ln(a)·u'
35
Choose the correct answer.
0
e+1
e-1
1
36
Choose the correct answer.
6
36
4
2
37
Choose the correct answer: ∫cos(x)
dx
sin(x) + C
sec(x) + C
cot2(x) + C
-sin(x) + C
38
Choose the correct answer: (d/dx)[cos(u)] =
cos2(u)·u'
sin(u)·u'
csc(u)·u'
-sin(u)·u'
39
Choose the correct answer.
6
2
7
4
40
Choose the correct answer.
y = -2(x - π/4)
y -1= -2(x - π/4)
y = 2(x - π/4)
y-1 = 2(x - π/4)
41
Choose the correct answer: ∫sin(x)
dx
sin(x)cos(x) + C
cos2(x) + C
-cos(x) + C
cos(x) + C
42
Choose the correct answer.
-1
1
-3
3
