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Calculus Solutions 23

# Calculus Solutions 23 - A-22 Answers t o Odd-Numbered...

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A-22 Answers to Odd-Numbered Problems Section 12.4 Polar Coordinates and Planetary Motion (page 468) 9 r \$ \$ + 2 2 g = O = L d ( r 2 \$ ) 1 1 ~ = . 0 0 0 4 r a d i a n s / s e c ; h = r 2 ~ = 4 0 , 0 0 0 r dt 47r2 150 1017 kg 1 3 mR x a; torque 15 T ~ / ~ ( G M / ~ ~ ) ' / ~ 1 7 4n2a3/T2G 19 ( 3 6 5 ~ ) 2 ~ 2 4 ) 1 ( ( 3 ~ 0 ~ 2 ( 6 6 6 7 ~ 1 0 0 1 1 23UseProbleml5 2 5 a + c = & , a - c = - ,&, solve for C, D 27 Kepler measures area from focus (sun) 29 Line; x = 1 10 3 3 r = 20 - 2t, 0 = z,v = -2ur + (20 - 2 t ) g u s ; a = (2t - 20)(%)~u, - 4(%)us; So lvldt CHAPTER 13 PARTIAL DERIVATIVES Section 13.1 Surfaces and Level Curves (page 475) 3 x derivatives ca, -1, -2, -4e-4 (flattest) 5 Straight lines 7 Logarithm curves 9 Parabolas 11 No: f = (x + y)" or (ax + by)" or any function of ax + by 1 3 f (x, y) = 1 - x2 - y2 1 5 Saddle 1 7 Ellipses 4x2 + y2 = c2 19 Ellipses 5x2 + y2 = c2 + 4cx + x2 2 1 Straight lines not reaching (1,2) 2 3 Center (1,l); f = x2 + y2 - 1 25 Four, three, planes, spheres 27 Less than 1, equal to 1, greater than 1 29 Parallel lines, hyperbolas, parabolas 3 1 \$ : 482 - 3x2 = 0, x = 16 hours 33 Plane; planes; 4 left and 3 right (3 pairs) Section 13.2 Partial Derivatives
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