TEAM PROJECT. Uniform Convergence. (a) Weierstrass M-test.
Chapter 15, Problem 15.5(choose chapter or problem)
TEAM PROJECT. Uniform Convergence. (a) Weierstrass M-test. Give a proof. (b) Termwise differentiation. Derive Theorem 4 from Theorem 3. (c) Subregions. Prove that uniform convergence of a series in a region C implies unifonn convergence in any portion of C. Is the converse true? (d) Example 2. Find the precise region ofconvergence of the series in Example 2 with x replacedby a complex variable z.(e) Figure 366. Show that x 2 ~;;'~1 (1 + x2 )-m = 1if x =F 0 and 0 if x = O. Verify hy computation that thepartial sums .1'10 S2' S3, look as shown in Fig. 366.-1y1osFig. 366. Sum 5 and partialsums III Team Project 18(e)
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