AP Calc BC formula quiz

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Calculus

49 Terms

1

definition of e

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2

definition of absolute value

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3

definition of the derivative

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4

alternative definition of the derivative

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5

definition of continuity

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6

average rate of change of f(x) on [a,b]

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7

intermediate value theorem

if f is continuous on [a,b] and k is any number between f(a) and f(b), then there is at least one number c between a and b such that f(c) = k

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8

what does d/dx [c] equal?

= 0

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9

derivative product rule

d/dx [f(x)g(x)] = f’(x)g(x) + f(x)g’(x)

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10

chain rule

d/dx (f(g(x))) = f’(g(x)) * g’(x)

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11

power rule

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12

quotient rule

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13

d/dx [sin u]

= cos u du/dx

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14

d/dx [cos u]

= - sin u du/dx

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15

d/dx [tan u]

= sec^2(u) du/dx

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16

d/dx [sec u]

= sec u tan u du/dx

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17

d/dx [csc u]

= -csc u cot u du/dx

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18

d/dx [cot u]

= - csc^2 (u) du/dx

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19

Rolle’s Theorem

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20

Mean Value Theorem (MVT)

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21

definition of a critical number

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22

definition of increasing functions

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23

definition of decreasing functions

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24

Test for Increasing and Decreasing functions

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25

First Derivative Test

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26

Second Derivative Test

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27

definition of definite integral

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28
<p>integral of …</p>

integral of …

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29

∫cos u du

sin u + c

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30

∫sin u du

-cos u + c

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31

∫sec²u du

tan u + c

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32

∫sec u tan u du

sec u + c

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33

∫csc²u du

-cot u + c

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34

∫csc u cot u du

-csc u + c

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35

first fundamental theorem of calculus

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36

second fundamental theorem of calculus

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37

integral chain rule

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38

average value of f(x) on [a,b]

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39

derivative of inverse function d/dx [(f^-1)(u)]

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40

d/dx [ln u]

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41
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42
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43
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ln |u| + C

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44

∫tan u du/dx

-ln |cos u| + C

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45

∫sec u du/dx

ln |sec u tan u| + C

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46

∫cot u du/dx

ln |sin u| + C

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47

∫csc u du/dx

-ln |csc u + cot u| + C

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48
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49
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