MAT-1120 Midterm: MATH 1120 App State Spring2009 Test3
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2 z f (x) dx ak = /24 points) taylor polynomials (a) let f (x) = ln(x). 2k + 1 x2k+1 g(100)(0) = g (0) = /15 points) fourier polynomials (a) let f (x) = x. Find the 1st-order fourier polynomial for f (x). (b) suppose the 2nd-order fourier polynomial for g(x) is q2(x) = 1 + 3 cos(x) 2 sin(2x) + 5 cos(2x). /16 points) an improper problem. (a) let f (x) = (cid:26) x 2 x 1 x < 1. Why or why not? (b) does r 0. Determine whether the following integrals converge or diverge. If they converge, you do not need to. If you use a comparison test, show your work. (a) does z 1. 1 ln|x| x dx converge or diverge? (b) does z . /14 points) the average annual precipitation on grandfather mountain is about 62 inches with a standard deviation of about 10 inches.
