MATH 2300 Quiz: Quiz13SolutionsS10
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November 18, 2008: use the maclaurin series for x sin x, show that. X k=0 ( 1)k(2k + 2) (2k + 1)! P k=0 sin x + x cos x. P k=0 d dx y x=1 y ( 1)k(2k+2) d dx ( 1)k (2k+1)!x2k+2. Y ( 1)k(2k+2) x=1 (2k+1)! converges to. sin(1) + cos(1) P k=0: use a similar method to determine what. Hint: construct a diagram similar to above, starting in the lower right, and. Ll in any expressions and operations, working counterclockwise. 2kk: solve the di erential equation y y = 0, suppose a solution to the di erential equation can be expressed as a power series: y = X k=0 (ak+2(k + 2)(k + 1) ak)xk. 0 = ak+2(k + 2)(k + 1) ak ak+2 = ak = a2 = a3 = a2k = ak (k + 2)(k + 1) ak 2 k(k 1) a0 a0. 3! a0 (2k)! a4 = a5 = a2.
