Derivative Rules
The product rule is
f'(x)g(x) + g'(x)f(x)
These are the 3 Integration Techniques only found in Calculus BC.
Improper Integrals, Linear Partial Fractions, and Integration by Parts
This test is used to determine if a series 1/n^p converges or diverges.
P-series test
L'Hospitals Rule is used when the limit of a function is either of these answers.
0/0 or infinity/infinity
The velocity vector at t = 2 given x(t) = 4t^3 and
y(t) = t^2 + 2t
(48,6)
The Quotient Rule is
f'(x)g(x)-g'(x)f(x) all over g(x)^2
The integral of e^x.
e^x +c
The first 4 nonzero terms of the Maclurin Series for cos(x).
1-(x^2/2!)+(x^4/4!)-(x^6/6!)
These are applied in order to evaluate the limit of a function using L'Hopital's rule.
the derivative of the numerator and derivative of the denominator of the original limit function
The general solution to the equation dy/dx = 3/(2y)
y=sq. root(3x+1) + C
The derivative of e^x
e^x
This technique should be used first before trying other techniques.
U-substitution
This determines divergence by the nth term test.
Any series who's limit as n->infinity equals anything other than zero
Daily Double: L'Hopital's rule was named after this French Mathematician
Guillaume-Francois-Antoine, Marquis de L'Hopital
This is the velocity of a particle who's position is given by f(x)=1/2 sin(x^2) at x=3 (Calculator)
-2.733
The slope of the line tangent to the equation f(x) = 4x^2 + 2 at x = 2
16
The average value of the function f(x) when f(x)=cos(x) from pi/2 to pi.
-2/pi
The sum of the geometric series 2(1/2)^n starting at n=1. (imagine that there is a series symbol there)
2
The limit of the function x2/ex as x approaches infinity.
zero
When given r = 2cos(theta), this is dy/dx.
2cos^2(theta) -2 sin^2(theta) all over -4cos(theta)sin(theta)
The derivative of cos(ln(2x^2)).
-sin(ln(2x^2)(2/x)
The indefinite integral of xsin2x
1/4 sin(2x)-1/2 x cos(2x) +C
The radius of convergence of the power series ((3x-2)^n)/n starting at n=0.
1/3
The limit as x->0 of (x^2)/(cos(x)-1)
-2
The integral of 2/(1+16x^2)
1/2 tan^-1(4x) +C