# AP Calculus BC - Stuff You Must Know

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L'Hôpital's Rule

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## Description and Tags

This includes a ton of stuff you must remember for the AP Test. It includes equations, theories, rules, derivatives, integrals, and more. I only recommend using these as flashcards or multiple choice only.

### 60 Terms

1

L'Hôpital's Rule

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2

Slope of a Parametric equation

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3

Euler’s Method

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4

Polar Area

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5

Polar Slope

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6

Integration by parts

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7

Integral of logarithms

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8

Ratio Test

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9

sin(2x)

2sin(x)cos(x)

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10

cos(2x)

cos^2(x) - sin^2(x)

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11

cos(2x)

1 - 2sin^2(x)

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12

cos^2(x)

1/2(1+cos(2x))

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13

sin^2(x)

1/2(1-cos(2x))

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14

sin^2(x) + cos^2(x)

1

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15

1+tan^2(x)

sec^2(x)

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16

cot^2(x) + 1

csc^2(x)

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17

sin(-x)

-sin(x)

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18

cos(-x)

cos(x)

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19

Taylor Series

f(x) = f(a) + f’(a)(x-a) + [f’’(a)(x-a)^2 / 2!] + [f’’’(a)(x-a)^3 / 3!] + …

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20

Lagrange Error Bound

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21

Maclaurin Series

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22

Alternating Series Error Bound

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23

Geometric Series

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24

sin(0)

0

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25

cos(0)

1

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26

tan(0)

0

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27

sin(pi/6)

1/2

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28

cos(pi/6)

root3/2

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29

sin(pi/4)

root2/2

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30

cos(pi/4)

root2/2

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31

sin(pi/3)

root3/2

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32

cos(pi/3)

1/2

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33

sin(pi/2)

1

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34

cos(pi/2)

0

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35

Chain Rule

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36

Product Rule

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37

Quotient Rule

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38

Trapezoidal Rule

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39

NEVER FORGET (for integrals)

+C

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40

Average Value

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41

d/dx sin(x)

cos(x)

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42

d/dx cos(x)

-sin(x)

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43

d/dx tan(x)

sec^2(x)

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44

d/dx cot(x)

-csc^2(x)

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45

d/dx sec(x)

sec(x)tan(x)

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46

d/dx csc(x)

-csc(x)cot(x)

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47

d/dx ln(u)

1/u

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48
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49

Solid Disk Method

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50

Solid Washer Method

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51

Cartesian Arc Length

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52

Polar Arc Length

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53

Parametric Arc Length

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54

Intermediate Value Theorem

If the function f(x) is continuous on [a,b], then f(x) achieves every value between f(a) and f(b) in the open interval (a,b).

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55

Mean Value Theorem

If the function f(x) continuous on [a,b], and the first derivative exists on the interval (a,b), then there is at least one number x = c in (a,b) such that f’(c) = [ f(b)-f(a) ] / (b-a).

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56

Rolle’s Theorem

Same as mean value theorem but if f(a) = f(b), then there is at least one number x = c in (a,b) such that f’(c) = 0.

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57

d/dx loga(x)

1/xln(a)

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58

Displacement

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59

Speed

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60

Distance

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