Calculus A/B: Integrals and Derivatives Flashcards

1

To find position from acceleration, you must...

Derive twice
Integrate once
Derive once
Integrate twice

2

d/dx 6xcos(3x+4)

6xsin(3x+4)
-18xsin(3x+4)
-6xsin(3x+4)
18xsin(3x+4)

3

d/dx e^2x

2ex
e2x
2e2x
4e2x

4

Choose the right answer

7
2
4
6

5

d/dx 2x

1
x2
2
x

6

What do you think you got in the exam

0 (for paul)
3
4 or 5
1 or 2

7

What does the mean value theorem state (for continuous, differentiable functions)?

average slope < 0
average slope > 0
average slope = instantaneous slope
average slope is not equal to instantaneous slope

8

∫ 1/4x+9 dx

1/4 ln|4x+9|+C
ln(4x+9)+C
1/4 ln(4x+9)+C
1/2 ln|4x+9|

9

The second derivative of a function provides information the ( ) of that function.

acceleration
speed
slope
concavity

10

d/dx 3xln(5x²)

15x3
1/x
3x/5x2
0.62739474

11

∫6^xdx

24x/ln24 + C
12x/ln12 + C
6x/ln6 + C
6x/ln6 + C

12

(d/dx)(sec(2x))

2sec(x)tan(x)
sec2(x)
tan2(x)
sec(x)tan(x)

13

f ^''(x)

-x
0
1
-1

14

d/dx sec^-1(x)

1/|x|(x2-1)0.5
1/(1-x2)50/100
-1/|x|(x2-1)0.5
1/|x|(x2-1)

15

f⁽²⁰⁰⁾e^x

e
e200
ex
200

16

Choose the correct answer

0
1
e-1
e+1

17

Choose the correct answer

36
2
4
6

18

d/dx log₁₂₆(3x)

(3x)(ln126)
3/(x)(ln126)
3log126(3x)
3/126x

19

∫(sec(x)tan(x))dx

tan2(x)/2 + C
tan(x) + C
sec(x) + C
sec2(x)/2 + C

20

d/dx -c

-1
x
1
0

21

f^'''(tan(x))

sec2(x)tan2(x)
4sec3(x)tan3(x)
-sec2(x)tan2(x)
sec6(x)tan2(x)

22

Choose the right answer

14
11
13
8

23

f^''(sin(x))

-cos(x)
sin(x)
cos(x)
-sin(x)

24

∫csc(x)cot(x)dx

-cot2(x) + C
sec(x) + C
-csc(x) + C
cot(x) + C

25

f^''(6x³+4x²-1)

18x2+8x
1
36x+8
2x2-4

26

d/dx 8^x

8x(ln8)
8
8x
8x(ln8)

27

Choose the correct answer

e(-t/2) + C
e(t/2) + C
e-t + C
2e(t/2) + C

28

d/dx (ln g(x))

g'(x)/g(x)
1/g(x)
1
g(x)/g'(x)

Calculus A/B: Integrals and Derivatives

Questions 28

Calculus A/B: Integrals and Derivatives

Questions 28