FM5002-HW5-2.22.12

# If z x sin z 2 y then f z x2 y2 x2 y2 2 xy 2 xy 2 u 1

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: y2 2 xy sin y2 x2 2 xy x2 . Therefore, x2 . y Sin x2 y2 a nd x V 0. FM5002−HW5−2.22.12.nb y 1 U 2 2 xy 2 y Cos x2 0042 14. Defin e f : 2 Define u, v : y2 by f z by f x y 2 xy 2 2 z y Cos x2 y2 2 xy 2 x Sin x2 y2 2 2 xy y x Sin x2 y2 . U hold. cos z . u x, y v x, y . Let U = u (x, y) an d V = v (x, y). a. Fin d U and V. b. Determin e whether the Cauchy Riemann equations x a. If z x x4 2 x2 y2 y4 y y x y2 2 x2 y, then f z x y x 2 x4 1 V 2 2 x2 y2 y4 y 2 b. They do n ot : y y4 y 2 Therefore, U but U 1 U x 4 x2 y 4 x3 2 4 y3 y 0042 15. Defin e f : 2 Define u, v : 4 x y2 by f x y y Sin x by f z y y cos x Van d y x V y 2 2 x2 y2 x4 x cos x x4 cos x a nd V y Cos x 1 Sin x 2 2 x2 y2 y4 1 x4 2 2 x2 y2 2 x2 y2 y4 cos x y 2 Cos x x4 y sin x sin x y4 y Sin x V y sin x y y y sin x . Sin x y Sin x , Sin x . cos z . u x, y v x, y . Let U = u (x, y) an d V = v (x, y). a. Fin d U and V. b. Determin e whether the Cauchy Riemann equations z a. If z x y, then f z xy cos z xy xy 2 y U cos x xy y U 1 2 y Van d x x y cos x sin x 2 and V sin x x y U hold. 2 xy y b. They do not : U z 2 2 x y . Sin x , but cos x 2 y 2 y y V 1 2 y y Sin x . sin x y . Therefore, 7 8 FM5002−HW5−2.22.12.nb 0042 16. Write x z y3 dx 3 y z dy z 4 x y z dz 8 2 x y z 3 dx in the form f x, y, z dx dy g x, y, z dx dz h x, y, z dy dz. xz 4y 3 dy y7 x d...
View Full Document

## This note was uploaded on 01/19/2014 for the course MATH 5002 taught by Professor Adams during the Spring '08 term at Minnesota.

Ask a homework question - tutors are online