This problem extends Example 5.14 and Exercise 5.19, allowing us to compute the following integrals simultaneously: For m e N, consider sin(x) dr x2m + 4280 cos(r) dr. r2m + 4280 and (a) Let f(2) = R> V4280. and z2m + 4280 Compute ff where or is the positively oriented semicircle formed by the line segment [-R, R] on the real axis, followed by the circular arc of radius R in the upper half plane from R to –R. DRAW STUFF, but don't prove anything for part (a). (b) Prove that limr-∞ Se. ƒ = 0. HINTS: Show |f(2)| < 2 for sufficiently large |z|. How large is |ei=| in the upper half plane?

This problem extends Example 5.14 and Exercise 5.19, allowing us to compute the following integrals simultaneously: For m e N, consider sin(x) dr x2m + 4280 cos(r) dr. r2m + 4280 and (a) Let f(2) = R> V4280. and z2m + 4280 Compute ff where or is the positively oriented semicircle formed by the line segment [-R, R] on the real axis, followed by the circular arc of radius R in the upper half plane from R to –R. DRAW STUFF, but don't prove anything for part (a). (b) Prove that limr-∞ Se. ƒ = 0. HINTS: Show |f(2)| < 2 for sufficiently large |z|. How large is |ei=| in the upper half plane?

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.3: Lines

Problem 22E

See similar textbooks