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A- 0 Answers to Odd-Numbered Problems CHAPTER 1 INTRODUCTION TO CALCULUS Section 1.1 Velocity and Distance (page 6) 2for 0 < t < 10 0 for 0 < t< T 1v = 30,0, -30;v = -10,20 3 v(t) = 1for 10 < t < 20 v(t) = for T < t < 2T -3for 20 < t < 30 0 for 2T < t < 3T 20for t < .2 20t for t 5 .2 5 25; 22; t + 10 7 6; -30 9 v(t) = { Ofor t > .2 1110%; l2\$% 29 Slope -2; 1 5 f 5 9 31 v(t) = 8 for O<t<T 8t for 0 5 t T -2 for T<t<5T lt) = { lOT - 2t for T 5 t _( ST 47 %v; ;V 49 input * input -+ A * A B * B C +I+ A +A --+ output B B + C A * A B A + B 61 3t+ 5,3t + 1,6t - 2,6t - 1,-3t - 1,9t - 4; slopes 3,3,6,6,-3,9 Section 1.2 Calculus Without Limits (page 14) 12 + 5 + 3 = 10; f = 1,3,8,11;10 3 f = 3,4,6,7,7,6; max f at v = 0 or at break from v = 1to -1 5 1.1,-2,s; f (6) = 6.6, -11,4; f (7) = 7.7, -l3,9 7 f (t) = 2t for t 5 5,10 + 3(t - 5) for t 2 5; f (10) = 25 9 7, 28, 8t + 4; multiply slopes 11f (8) = 8.8, -15,14; = 1.1,-2,5 13 f (z) = 3052.50 + .28(x - 20,350); then 11,158.50 is f (49,300) 15 19+% 17 Credit subtracts 1,000, deduction only subtracts 15% of 1000 19 All vj = 2;vj = (-l)j-';vj = (\$)j 21 L's have area 1,3,5,7 23 fj = j; sum j2 + + 25 (1012 - 9g2)/2 = 7 27 Vj = 2j 29 f31 = 5 31 aj = - fj 35 0; 1; .1 35 v = 2,6,18,54; 2 3j-I 37 = 1,.7177, .6956, .6934 -+ ln 2 = .6931 in Chapter 6 39 V, = -(i)j 41 vj = 2(-l)j, sum is - 1 45 v = 1000,t = lO/V 47 M, N 51 4 < 2.9 < 92 < 29; (i)2 < 2(i) < @ < 2lI9 Section 1.3 The Velocity at an Instant (page 21) 16,6,ya,-12,0,13 34,3.1,3+h,2.9 5Velocityatt=lis3 7Areaf=t+t2,slopeoffis1+2t 9 F; F; F; T 112; 2t 13 12 + 10t2; 2 + lot2 15 Time 2, height 1,stays above from t = \$ to 17 f(6) = 18 21 v(t) = -2t then 2t 23 Average to t = 5 is 2; v(5) = 7 25 4v(4t) 27 v, = t, v(t) = 2t Section 1.4 Circular Motion (page 28) 1lor, (0, -11, (- 1,O) 3 (4 cos t, 4 sin t) ; 4 and 4t; 4 cos t and -4 sin t 5 3t; (cos 3t, sin 3t); -3 sin 3t and 3 cos 3t 7 z = cost; J2/2; -&/2 9 2x13; 1; 2a 11Clockwise starting at (1,O) 13 Speed \$ 15 Area 2 17 Area 0

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Answers to Odd-Numbered Problems A- 1 19 4 from speed, 4 from angle 21 from radius times 4 from angle gives 1in velocity 23 Slope i; average (1 - \$)/(r/6) = = .256 25 Clockwise with radius 1from (1,0), speed 3 27 Clockwise with radius 5 from (0,5), speed 10 29 Counterclockwise with radius 1from (cos 1,sin I), speed 1 31Left and right from (1,O) to (-1,0), u = - sin t 33 Up and down between 2 and -2; start 2 sin 8, u = 2 cos(t+8) 36Upanddownfrom(O,-2)to(0,2);u=sinit 37~=cos~,~=sin~,speed~,u~,=cos~ 360 Section 1.5 A Review of Trigonometry (page 33) 1Connect corner to midpoint of opposite side, producing 30' angle 3 n 7 \$ -r area ir28 9 d = 1,distance around hexagon < distance around circle 11T; T; F; F 13cos(2t+t) = cos2tcost -sin2tsint = 4cos3t - 3cost 15icos(s-t)+~cos(s+t);~cos(s-t)-icos(s+t) 17cos8=secB=~tlat8=nr 19Usecos(t-s-t)=cos(t-s)cost+sin(t-s)sint 238=~+rnultipleof2n 25 8 = f+ multiple of n 27 No 8 29 4 = f 31 lOPl= a, 1OQ1= b CHAPTER 2 DERIVATIVES Section 2.1 The Derivative of a Function (page 49) 1(b) and (c) 3 12 + 3h; 13 + 3h;3; 3 6 f(x) + 1 7 -6 9 2x+Ax+ 1;2x+ 1 -4 11&d=&+3- 137;9;corner 15A=1, B=-1 17F;F;T;F 19 b = B; m and M; m or undefined 21 Average x2 + xl + 2x1 25 i; no limit (one-sided limits 1,-1); 1; 1if t # 0, -1 if t = 0 27 ft(3); f (4) - f (3) 29 2x4(4x3) = BX7 31 = l= 2 33 X=-L. ,, f1(2) doesn't exist d~ 2u 2fi AX 36 2 f 5 = 4u32 Section 2.2 Powers and Polynomials (page 56) 15 3x2 - 1 = 0 at x = fi and A 17 8 ft/sec; - 8 ft/sec; 0 19 Decreases for -1 < x < fi z+h)-x 23 1 5 10 10 5 1adds to (l+l)'(x = h = 1) 253x2;2hisdifferenceofx's 27% =2x+Ax+3x2+3xAx+(Ax)2 +2x+3x2=sumofseparatederivatives 1 4 1 297~~;7(x+l)~ 31~x4pl~~anycubic 33x+~x2+\$x3+fx4+C 35~x,120x6 37 F; F; F; T; T 39 = .12 so 4 = i(.12); sixcents 41 4 = 1 C- * = -3 + A Adz 43E=X 1 10. lXn+l. 2x+3 45ttofit 47i5x ,n+l ,dividebyn+l=O Section 2.3 The Slope and the Tangent Line (page 63)
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