BC Calc Things to Memorize - All Units

Power Rule

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 e^x

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