APPM 2350 Midterm: appm2350summer2017exam3_0
Document Summary
Summer 2017: (18 pts) evaluate z 1. 0: (20 pts) consider the solid between two concentric spheres of radii r1 and r2 with 0 < r1 < r2. The mass density of the solid varies inversely with the cube of the distance from the center of the spheres, that is, mass density = k/(distance3). Rpx2 + y2 z h, 0 y r2 x2o where h: (12 pts) let w = n(x, y, z) r3(cid:12)(cid:12)(cid:12) r x 0, h and r are positive constants. Change of variables f (x, y) da = zz. Taylor series f (x, y) = f (a, b) + fx(a, b)(x a) + fy(a, b)(y b) 2! (cid:2)fxx(a, b)(x a)2 + 2fxy(a, b)(x a)(y b) + fyy(y b)2(cid:3) 3! (cid:2)fxxx(a, b)(x a)3 + 3fxxy(a, b)(x a)2(y b) + 3fxyy(a, b)(x a)(y b)2 + fyyy(a, b)(y b)3(cid:3) + .
