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Formulas and concepts to memorize for the AP Calc BC exam. For more detailed integration flash cards, see my BC Calc Things to Memorize Unit 6 study set.

1

Power Rule

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2

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3

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4

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5

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7

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8

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9

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10

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11

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12

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13

Low D high minus high D low, draw the line and square it below

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14

Derivative of the outside function times the derivative of the inside function

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15

Definition of derivative

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16

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17

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18

Integration by parts

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19

Lâ€™Hopitalâ€™s Rule

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20

First fundamental theorem

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21

Second fundamental theorem

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22

Alternating series error bound

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23

Lagrange error bound

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24

McLaurin series for e^{x}

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25

McLaurin series for sin(x)

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26

McLaurin series for cos(x)

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27

Taylor series centered at x=a

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28

Logistic differential equation

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29

Logistic equation

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30

Rolles Theorem

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31

Average value of a function

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32

Mean Value Theorem

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33

Intermediate value theorem

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34

Arc length (cartesian function)

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35

Arc length (parametric function)

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36

Speed (parametric function)

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37

Polar area

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38

First derivative of a parametric function

note: this is the same for polars, just with theta instead of t

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39

Second derivative of a parametric function

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40

Polar conversions

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41

nth term test

Cannot be used to prove convergence

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42

geometric series test

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43

p-series test

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44

Alternating series test

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45

Integral test

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46

Ratio test

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47

Direct comparison test

A series with smaller terms than a known convergent series will also converge

A series with larger terms than a known divergent series will also diverge

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48

Limit comparison test

usually compared to a p-series

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49

conditions for a functionâ€™s continuity at a point

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50

power series for 1/(1-x)

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51

Washer method (revolved volume of an areas between two curves)

where R(x) is outer radius and r(x) is inner radius

dx for around the x-axis or other horizontal line

dy for around the y-axis or other vertical line

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52

Squeeze theorem

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53

Extreme value theorem

If f(x) is continuous on [a,b] then it must have an absolute maximum value and an absolute minimum value on that interval

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54

Trapezoidal Riemann Sum

Overestimate when concave up

Underestimate when concave down

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55

Sum of a geometric series

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56

Relationship between f and its first two derivatives (for derivative tests)

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57

Displacement

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58

Total distance

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59

Current position

where s(a) is initial position

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60

Speed

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61

Volume with cross-sections

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62

Special limit property for sine

note that x may be a quantity (such as 4x) as long as itâ€™s the same in the numerator and denominator

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63

Special limit property for cosine

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