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- 3. Show that II (1+22) is absolute convergent if and only if |z| < 1. Show k=0 that the product converges to 4. Show that 1+sin( is absolute and uniform convergent for all 2. k=0 5. Show that Res(T(2);-n) = (-1)" n!M1. S sin² dx is convergent because sin < sin² x and f sin² x dx is convergent. 1+z² 1+x² Jury 2. sin da is convergent because in and fi da is convergent. roo x 1+z² 1+x² 12 1+z² 3. sin da is convergent because inperiod -π ≤ t ≤ π. The following f(t) is a periodic function of period T = 27, defined over the -2 2 when when 0 < t ≤π -Show COMPLETE solutions. Box the FINAL answer.Q7. A-Indicate the order of the pole at z-0 for (sin(z)+sinh(z) — 2z)², B- Find the first four terms of the Laurent series expansion of f(2)= z(1²+1) in the setAsap plz handwritten solution acceptable Urgent plz8.1 Define what it means for a series E1 an to converge. 8.2 Let f : [1, 00) → [0, 0) be continuous and decreasing. Show that the series E=1ªn where f(n) = an, converges if and only if the improper integral f(x) dx con- verges.Let 3nv5 2n3 +n 6n + 2n2- 1 Yn 6nvi + 4n3 -8 3n (2n + 1) 2n7 and Z, =1- sin Note: Here the main problem is finding the explicit limit. O A. The sequences Wn and Y converge to oo and 1, respectively while Z diverges O B. The sequences Wn and Y, converge to 0 and oo, respectively while Zn converges to 1 O c. The sequences W and Y converge to 0 and 6, respectively while Z, converges to 1/2. O D. The sequences Wn and Y converge to -1/2 and oo, respectively while Z converges to 0. O E. The sequences Wn and Y converge to 1/2 and 0, respectively while Z, diverges O F. The sequences W and Y converge to -1/2, and 1, respectively while Z divergesSEE MORE QUESTIONSRecommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, Incorporated
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