According to the extreme value theorom, what must exist if a function is continuous on a closed interval?
An absolute max and min.
200
What is the derivative of x³ at x=2?
12
200
∫(4x³+1)dx over the interval [0,5]
630
200
d/dx cot^-1(x)
-1/(x²+1)
200
What is the area of the region bounded by y=-x² +x+6 and y=4?
9/2
200
What conditions must be in place for mean value theorom to be valid?
f has to be continuous and differentiable on the interval (a,b)
300
What is the derivative of 2x(x²+1)?
6x²+2
300
∫((3x²+1)/(x³+x))dx
ln|x³+x|+c
300
∫dx/√1-x² over the interval [-1/2,1]
2π/3
300
The region enclosed by the line x+y=1, the x axis, and the y axis is rotated about the line y=-1. What is the volume of the solid created?
4π/3
300
What conditions must be in place for the fundamental theorom of calculus to be valid?
f has to be continuous on the interval (a,b) and F(x) has to be an antiderivative of f(x)
400
What is the derivative of x²/(x³+1)?
(2x-x^4)/(x³+1)²
400
∫3^x dx
(3^x/ln3)+c
400
d/dx sec^-1(x)
1/ |x|√x²-1
400
The base of a solid is the region enclosed by the graph of y=3(x-2)², x=0, and y=0. If the cross sections are squares perpendicular to the x axis, what is the volume of the solid?
57.6
400
If f is continuous on the interval (a,b) and k is any number between f(a) and f(b) then what has to be true?
There is at least one number(c) between a and b such that f(c)=k
500
What is the derivative of (2x(x² +1))/(x³+1)?
(-8x^5-4x³-2x²+2)/(x³+1)²
500
∫dx/(xlnx)
ln|lnx|+c
500
∫cosx3^sinx dx
(3^sinx/ln3)+c
500
A region is bounded by y=x²/2, y=8, and the y axis. What is the volume of the solid created when this region is rotated about the y axis?
64π
500
What conclusion does rolles theorom come to when f is continuous and differentiable on the interval (a,b) and f(a)=f(b)?
There exists a number(c) on the interval (a,b) where f'(c)=0