AP Calculus BC - Mathfacts
What is the hypothesis of the integral test
Positive terms Continuous Decreasing
Write the equations to find arc length for rectangular parametric and polar functions.
Rectangular: Integral of sqrt(1+(dy/dx)^2) Parametric: Integral of sqrt((dx/dt)^2 + (dy/dt)^2) Polar: Integral of sqrt(r^2+(dr/dtheta)^2)
What's a p-series? When do p-series converge?
Sigma 1/n^p p>1
Write the formula to find the sum of a geometric series.
a/(1-r) |r| < 1
What's the sum of the alternating harmonic series?
ln2
Write an equation for half life.
t = ln2/k
Write the equation for Euler's method.
yn+1 = yn +hf(xn, yn)
Draw a quick sketch for r = cos(2theta)
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Write an equation for Lagrange error bound
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Write an expression using sigma for a Maclaurin series.
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Write the first four terms, the general term, the sigma expression and the interval of convergence for each of the following.
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Write an equation to find the polar area
Integral (1/2*sqrt(r^2))
Show that the harmonic series diverges
Integral test from 1 to infinity.
Write the equation for integration by parts.
Integral udv = uv-Integral vdu
Write an integral to find total distance traveled.
Integral |v(t)|dt
What is the alternating series test
Limit of an+1 as n goes to infinity = 0. Series is decreasing.
Write the equation for Newton's law of cooling as a differential equation and as a function.
dT/dt = -k(T-Ta) T(t) - Ta = (T0-Ta)e^-kt
Write the formulas for solving first order linear differential equations using the integrating factor method.
dy/dt + p(t)y = q(t) u = e^(Integral p(t)dt) Y = (Integral u(t)g(t)dt + C)/u(t)
Write the equation for the logistic model as a differential equation and as a function.
dy/dt = k(1-y/l) and Y = ((y0)L)/(y0+(l-y0)(e^-kt))
Write the differential equation and solution for exponential growth and decay
dy/dx = ky y = y0*e^(-kt)
Write an equation to find the speed for parametric equations
sqrt((dx/dt)^2+(dy/dt)^2)
Write equations to change from polar to parametric
x = rcos(theta) y = rsin(theta)
Write an equation for the error in an alternating series.
|S-Sn| <= an+1