Formulas & Theorems
Sum it Up
Derivatives
A Function Does What?
Rotate This
100
d/dx[f(x)g(x)]= f(x)g'(x)+g(x)f'(x)
What is Product Rule
100
given n=4 approximate the integral from 2 to 10 using a right reimman sum
What is 158
100
d/dx [ 2 sin(x)cos(x) ] in the most simplified form
What is 2 cos(2x)
100
f'(x) > 0
What is the function is increasing
100
This is the volume of the area bounded between the curves f9x)=x^3-8 and g(x)=-x^2-1 rotated around the x-axis. (Problem donated by Eric Lacroix)
What is 493.7000611
200
d/dx [ f(g(x))] = f'(g(x)) g'(x)
What is Chain Rule
200
given n=3 approximate the integral from 2 to 8 using a trapezoidal sum
What is 64
200
Given f(x)=(3x+1)^(1/2) Find f'(5)=
What is 3/8
200
f'(c) = 0 and f'(x) changes sign from negative to positive at x=c
What is c is a relative minimum
200
An area is bounded by f(x)=x^2-4 and the x-axis. Find the volume created by cross sections that are squares.
What is 512/15 or 34.133
300
f'(c) = f(b)-f(a)/ b-a , only if f(x) is continuous and differentiable on [a,b]
What is Mean Value Theorem (MVT)
300
given n=3 approximate the integral from 8 to 14 using a left Reimann Sum
What is 224
300
Given f(x)= (x+3)/x Find the equation of the tangent line to the curve at the point (1,4)
What is y-4=-3(x-1) or y=-3(x-1)+4 or y=-3x+5
300
f"(x) < 0
What is the function is concave down
300
This is the Volume when the area bounded by the functions f(x)=(x+1)^(1/2) and g(x)=4-x^(1/2) is rotated about the line y=-1.
What is 93....
400
lim as h->0 of f(x+h)-f(x) / h
What is Definition of the Derivative
400
given n=3 approximate the integral from 2 to 14 using a midpoint sum
What is 300
400
d/dx [ 4xy+y^3=2x ]
What is (2-4y)/(3y^2+4x)
400
if the limit of f(x) as x approaches zero exists but f(0) DNE
What is the function is disconintuous
400
This is the volume of the area between the graphs of f(x)=2sin(x) and g(x)=2cos9x)-.08 rotated about the x-axis. (Problem donated by John Sullivan)
What is .9578pi or 3.009
500
d/dx of the integral from c to g(x) of f(t) = f(g(x)) g'(x)
What is Fundamental Theorem of Calculus (FTC)
500
given n=6 approximate the integral from 2 to 14 using a trapezoidal sum
What is 313
500
find f'(pi/8) Given f(x)= (cos(2x))2
What is -1/2
500
f'(c)=0 and f"(c)>0
What is f(c) is a relative minimum
500
This is the volume of the area bounded by y=x^3 and y=x(in the first quadrent) rotated about the y-axis
What is .837759
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