Compute the Taylor series for f(x)= sq root (x) about x=1. Determine where the series sconverges absolutely, converges conditionally, and diverges. Hint: 2(k!)=2*4*6...(2k-2)*2k. Also 1<2, 3<4, 5<6,..., 2k-1<2k should help you out with a comparision.
Wow, that's pretty interesting, certainly. Just reviewing the concepts of surface integrals. Thanks for all the input, these problems never cease to amaze me.
For a planet of radius a, find the area of the surface between the equator and latitude 60 degress north.
This problem was posed to me way back in my calc II class. Instructor (somehow :wink: ) used series to solve it, then asked us if we could solve it differently. I only vaguely remember...
Compute the sum from k=0 to infinity of (k+1)(x)(1-x)^k.
I don't have any ideas about how to start this one, except that perhaps it resembles a geometric series? Also we're supposed to use the power series for 1/x which we know to be (1-x)^k. (That's all I could figure out on my own so far)...
Determine wheter the sum from n=2 to infinity of ((-1)^(n+1))/(ln(n)) converges absolutely, converges conditionally, or diverges. Also assume you have a supercomputer that can add 10^15 terms per second (which is very fast for even a supercomputer). If you wanted to estimate the sum to within...