If f is continuous on the closed interval a to b, then there exists a number c in the closed interval a to b such that the integral from a to b of f(x) is equal to f(c)(b-a). What is this called?
What is the Mean Value Theorem.
100
1 + x + x^2 + x^3 + ... + x^n + ... is the series for _____.
What is 1/(1-x)
100
V=pi int ([R(x)]^2-[r(x)]^2])
What is the washer method
100
This is equal to x in a polar function.
What is rcosθ
200
The type of line that passes through a curve at x=a and has a slope m=-1/F '(a)
What is a normal line?
200
Find the integral of (secx)^2 from 0 to pi/4
What is 1
200
This maclaurin series has a domain of all real numbers and is modeled by the function x^n/n!.
What is e^x
200
This method is used to find the limit of a function by taking the derivative(s) of the numerator and denominator of the function.
What is L'Hopitale's rule?
200
The velocity vector of a function is <2t, cos4t>
What is its acceleration vector.
<2, -4sin4t>
300
The derivative of f(x)=(sin(4t))^3
What is 12(sin(4t))^2)(cos(4t))
300
The basic integration formula for the integral of (a^u)du
What is [1/(ln(a)](a^u) + c
300
The series 1/n^p converges when p> 1 and diverges for 0
What is the P-series test?
300
This is used to estimate the y-value of a function by taking the previous y-value and adding it to the slope at that point multiplied by the step size used.
What is Euler's Method?
300
This formula is used to find the area of a polar function.
What is A= 1/2 int [f(θ )]^2 dθ
400
u'/ l u l (u^2 - 1)^(1/2) is the derivative of _______.
What is arcsec(u)
400
Find the integral of sinx/[(cosx)^2]
What is secx + c
400
The value of this function is modeled by the series:
1+ 1/6 + 3/40+ 8/336............
What is arcsin(1)
400
Where f(x)= e^-3x . Find the arc length from the interval x=1 to x=6
5
400
This function is a lima con with an inner loop that is symmetrical about the y-axis.
What is a +/- bsinθ where a/b <1
500
The tangent line to the graph given by x^2((x^2)+(y^2))=y^2 at the point (sqrt(2)/2, sqrt(2)/2)
What is y= 3x-sqrt(2)
500
Find the integral of arctan(4x)
What is xarctan(4x) - [ln((16x^2)+1)]/8 + c
500
The maclaurin series for ln(1+x) is ______.
What is x - x^2/2 + x^3/3 + x^5/5 - ... + [(-1)^n]((x^n)/n) + ...
500
Find the volume of the region rotated about the line y= -3 bounded by the region 1/ sqrt (x +2), y=0 x=0 and x= 5
191.735
500
Find the horizontal and vertical tangents of r=2sin(theta)