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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.
Power Rule
Low D high minus high D low, draw the line and square it below
Derivative of the outside function times the derivative of the inside function
Definition of derivative
Integration by parts
L’Hopital’s Rule
First fundamental theorem
Second fundamental theorem
Alternating series error bound
Lagrange error bound
McLaurin series for ex
McLaurin series for sin(x)
McLaurin series for cos(x)
Taylor series centered at x=a
Logistic differential equation
Logistic equation
Rolles Theorem
Average value of a function
Mean Value Theorem
Intermediate value theorem
Arc length (cartesian function)
Arc length (parametric function)
Speed (parametric function)
Polar area
First derivative of a parametric function
note: this is the same for polars, just with theta instead of t
Second derivative of a parametric function
Polar conversions
nth term test
Cannot be used to prove convergence
geometric series test
p-series test
Alternating series test
Integral test
Ratio test
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
Limit comparison test
usually compared to a p-series
conditions for a function’s continuity at a point
power series for 1/(1-x)
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
Squeeze theorem
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
Trapezoidal Riemann Sum
Overestimate when concave up
Underestimate when concave down
Sum of a geometric series
Relationship between f and its first two derivatives (for derivative tests)
Displacement
Total distance
Current position
where s(a) is initial position
Speed
Volume with cross-sections
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
Special limit property for cosine
Note 
Flashcard (39)