Question

ry 82. Let f(x, y) - 0 if (x, y)-0 The graph of f is shown on page 813. a. Show that j x,0) - x for all x, and a0, y) y for all y. b. Show that (0, 0) ахау (0, 0) The three-dimensional Laplace equation dy dx is satisfied by steady-state temperature distributions T-f(x, y, z) in space, by gravitational potentials, and by electrostatic poten- tials. The two-dimensional Laplace equation ar'ду obtained by dropping the a2f/az2 term from the previous equation, describes potentials and steady-state temperature distributions in a plane (see the accompanying figure). The plane (a) may be treated as a thin slice of the solid (b) perpendicular to the -axis Boundary temperatures controlled

Answer 1

(xo) = 2 fos all X オ2442

15%99, 2-2) as both oe -ve equal 2 2. Hen proveo