BC Calc Things to Memorize - All Units

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<p>Power Rule</p>

Power Rule

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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.

63 Terms

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<p>Power Rule</p>

Power Rule

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

<p>Low D high minus high D low, draw the line and square it below</p>
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Derivative of the outside function times the derivative of the inside function

<p>Derivative of the outside function times the derivative of the inside function</p>
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<p>Definition of derivative</p>

Definition of derivative

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Integration by parts

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19

L’Hopital’s Rule

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<p>First fundamental theorem</p>

First fundamental theorem

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<p>Second fundamental theorem</p>

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 ex

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25

McLaurin series for sin(x)

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McLaurin series for cos(x)

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Taylor series centered at x=a

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Logistic differential equation

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Logistic equation

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30

Rolles Theorem

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31

Average value of a function

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Mean Value Theorem

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Intermediate value theorem

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34

Arc length (cartesian function)

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Arc length (parametric function)

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Speed (parametric function)

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Polar area

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First derivative of a parametric function

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

<p>note: this is the same for polars, just with theta instead of t</p>
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Second derivative of a parametric function

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Polar conversions

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41

nth term test

Cannot be used to prove convergence

<p>Cannot be used to prove convergence</p>
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geometric series test

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p-series test

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Alternating series test

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Integral test

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Ratio test

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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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Limit comparison test

usually compared to a p-series

<p>usually compared to a p-series</p>
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49

conditions for a function’s continuity at a point

<p></p>
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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

<p>where R(x) is outer radius and r(x) is inner radius</p><p>dx for around the x-axis or other horizontal line</p><p>dy for around the y-axis or other vertical line</p>
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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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Trapezoidal Riemann Sum

Overestimate when concave up

Underestimate when concave down

<p>Overestimate when concave up</p><p>Underestimate when concave down</p>
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Sum of a geometric series

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

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Displacement

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Total distance

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Current position

where s(a) is initial position

<p>where s(a) is initial position</p>
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Speed

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Volume with cross-sections

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Special limit property for sine

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

<p>note that x may be a quantity (such as 4x) as long as it’s the same in the numerator and denominator</p>
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63

Special limit property for cosine

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