Calculus Solutions 28

Calculus Solutions 28 - Answers t o Odd-Numbered Problems $...

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Answers to Odd-Numbered Problems f dx dz, & $ gives aeros; = dy dz, f $: = I: - I," f 25 I = J:~(~~ + z2)dx dy dz = y; J/I x2dv = t; 3 $JJ(x $!, $:, 27 - T)2d~ = 29 J: dx dy dz = 6 $1Tkape~oidalrule is second-order ; correct for 1,x, y, z, xy, xz, yz, xyz Section 14.4 Cylindrical and Spherical Coordinates (page 547) 1 (r, 8, 2) = (D, 0, 0); (P, 498) = (Dl :, 0) 3 (r, #,a) = (0, any angle, Dl; (P, 4,8) = (D,0, any angle) 5(x,y,z)=(2,-2,2fi);(r,8,~)=(2@,-f,2@) 7(x,y,z)=(O,O,-l);(r,d,z)=(O,anyangle,-1) 9 4 = tan-'(:) 11 45' cone in unit sphere: y(1- A) 13cone without top: 2 15 hemisphere: 17 $ 19Hemisphere of radius r : :r4 21 r(R2 - z2); 4rt-dn 23 $a3 tana (see 8.1.39) = p-DcOsC - near lide - Q hypotenuse = COs 31 Wedges are not exactly similar; the error is higher order + proof is correct 33 Proportional to 1 + i(\/02 + (D - h)2 - @TP) a cos8 -rsin# 0 35 J = b = abc; straight edges at right angles 37 sin 8 r cos 8 0 = r C 0 0 1 3g e. n 3 '3 41 p3; pa; force = 0 inside hollow sphere CHAPTER 15 VECTOR CALCULUS Section 15.1 Vector Fields (page 554) lf(z,y)=x+2y 3f(x,y)=sin(x+y) 5f(x,y)=ln(x2+#)=21nr 7 F =
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This document was uploaded on 11/02/2011 for the course MAC 2311 at University of Florida.

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