Grab Bag!
What is integral of a to b of |r(t)|dt?
The standard form for complex numbers
What is a + bi?
The variables used as coordinates for polar coordinates
What is r and theta?
The antiderivative of 1/(1+x2)
What is arctanx +C?
What is the general term?
The approach for a trig integral with secmx and tannx where the power of m is even and at least 2
What is converting all but 2 powers of sec to tan using Pythagorean identities and using u-sub with u=tan?
i19
What is -i?
What is -1/2?
What is -2 to 0 and 0 to 3?
A Taylor Series centered at c = 0
What is a Maclaurin Series?
The amount of water that flows into a tank between t=1 minute and t = 5 minutes if the rate of flow is r(t)=t2 ft3/min
What is 124/3 ft3?
the polar form of z = 9 (as a complex number!)
What is z = 9(cos(pi)+isin(pi))?
The formula for polar area
What is A = integral of (1/2)r2d(theta)?
The trig substitution for x5/(36x2+1)3/2
What is x = (1/6)tany and dx = (1/6)sec2y dy?
(note y is used in place of theta)
A series with a common ratio larger than or equal to 1
What is a diverging geometric series?
The decomposition of 8/(3x3+7x2+4x)
What is [2/x] + [18/(3x+4)] - [8/(x+1)]?
(3+3i)5
What is -972-972i?
The values of theta for which r = -1 (within the first 2pi) for the function r(theta)=2cos(theta)-1
What are pi/2 and 3pi/2?
An appropriate comparison for the integral from 3 to infinity of 1/(x-e-x)
(Specify the name of the test we are doing, whether the comparison is larger or smaller, and what this means for the test!)
What is 1/x < 1/(x-e-x) where the integral diverges by the Direct Comparison Test?
A series of an for which the series of |an| also converges
What is an absolutely convergent series?
The interval and radius of convergence for the series of [(n+1)/(2n+1)!](x-2)n
What is (-infinity, infinity) and R=infinity?
All roots of (2i)1/2
Whate are 1+i and -1-i?
The points of intersection of r = 1-sin(theta) and r=2+sin(theta)
What are -pi/6 (or 11pi/6) and 7pi/6?
The dv, u, du, and v for the integral of (lnx)dx
What is dv=dx, u=lnx, du= 1/x dx, v=x?
A convergence test with three rules for interpreting the results (for full points you must also identify the results!):
1) L = 0
2) L = C >0
3) L = infinity
What is the limit comparison test?
1) If sum bn converges, sum an also converges
2) sum an and sum bn both converge or both diverge
3) if sum bn diverges, sum an also diverges