Consider the following maps from the closed unit diskD = {(x, y) E R? : x² + y² < 1} in R2 to itself:%3Df(r. y) = ()g(x, y):%3Dh(x, y) = (xy, y)%3DWhich maps have exactly one fixed point in D?Only f and g.O Only g and h.Only h and f.All of f, g, and h.

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Answered: Consider the following maps from the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Show that f dx + gdy + h dz = (-1,–5,–3) (5,–1,2) SE 12- (4xy:4dæ + 6y²a?z*dy+ 82y³a²dz) is independent of path: r(-1,–5,–3) J(5,–1,2) ah -241,2,3 -242,2,3 az af -16ry3,3 az ah -16x3,3 dg -12y2,4 %3D af %3D ду -1212,4 Therefore curl F = r(-1,–5,–3) J(5,–1,2) -(4xy°z*dx + 6y?a²z*dy+ 82°y°x*dz) = [U

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Consider the following maps from the closed unit disk D = {(x, y) E R? : x? + y < 1} in R? to itself: %3D f(x. ) = () g(x, y) = %3D h(x, y) = (xy, y) %3D Which maps have exactly one fixed point in D? Only f and g. O Only g and h. Only h and f. All of f, g, and h.