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Calculus review Flashcards | StudBud
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Calculus review
Calculus review
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Questions
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Answers
1
Choose the correct answer: (d/du)[sin(u)] =
tan(u)
-tan(u)
cos(u)
-cos(u)
2
Choose the correct answer: (d/du)[
e
u
] =
eu + C
-ueu
eu
ueu
3
Choose the correct answer.
-1 < x < 3
All values of x
x < -1 and x > 3
-3 < x < 1
4
The second derivative of a function provides information about the _______ of that function.
acceleration
concavity
speed
slope
5
To find velocity from position, you must...
find the 1st derivative
integrate once
find the 2nd derivative
integrate twice
6
Choose the correct answer.
-3
-1
3
1
7
Choose the correct answer.
y-1 = 2(x - π/4)
y = 2(x - π/4)
y -1= -2(x - π/4)
y = -2(x - π/4)
8
Choose the correct answer: (d/du)[cos(u)] =
-sin(u)
tan(u)
cos2(u)
sin(u)
9
Choose the correct answer: (d/du)[
ln(u)
] =
ueu
(1/u)
ln(u)
(1/u)∙ln(u)
10
Choose the correct answer: ∫cos(x)
dx
-sin(x) + C
sin(x) + C
sec(x) + C
cot2(x) + C
11
Choose the correct answer: ∫
e
x
dx
xex
ex
xex + C
ex + C
12
What does the mean value theorem state (for continuous, differentiable functions)?
average slope ≠ instantaneous slope
Average slope < 0
average slope = instantaneous slope
average slope > 0
13
Choose the correct answer.
e-1
0
1
e+1
14
Choose the correct answer.
14/3
28/3
32/3
16/3
15
Choose the correct answer.
6x2sin(x3)cos(x3)
-6x2sin(x3)
-6x2sin(x3)cos(x3)
6x2cos(x3)
16
Choose the correct answer.
2
6
7
4
17
How do you find the area between two functions of x?
top - bottom
∫(bottom - top)dx
π(top + bottom)
∫(top - bottom)dx
18
The first derivative of a function provides information about the _______ of that function.
concavity
slope
speed
acceleration
19
Choose the correct answer: ∫sin(x)
dx
sin(x)cos(x) + C
cos2(x) + C
cos(x) + C
-cos(x) + C
20
For all related rates problems, you must derive each term with respect to
area
volume
time
x
21
Choose the correct answer.
7/27
-7/27
25/27
-25/27
22
Choose the correct answer.
36
2
4
6
23
Choose the correct answer: ∫(1/x)
dx
2x-2 + C
ln∣x∣ + C
xn+1 + C
x-2 + C
24
To find position from acceleration, you must...
find the 1st derivative
integrate once
find the 2nd derivative
integrate twice
25
Choose the correct answer.
e-t + C
e(-t/2) + C
2e(t/2) + C
e(t/2) + C
26
Choose the correct answer.
16π/3
8π/3
32π/5
4π/3
27
Choose the correct answer.
11
14
13
8