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Calculus Solutions 3

# Calculus Solutions 3 - A 2 Answers t o Odd-Numbered...

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A- 2 Answers to Odd-Numbered Problems 17 (-3,19) and (8, E) 1 9 c = 4, y = 3 - x tangent at x = 1 21 (1 + h)3; 3h + 3h2 + h3; 3 + 3h + h2; 3 23 Tangents parallel, same normal 25 y = 2ax - a2, Q = (0, -a2) ; distance a2 + i ; angle of incidence = angle of reflection fi' 2 7 ~ = 2 p ; f o c u s h a s y = \$ = p 2 9 y - & = x + L - x = - 2 - 4 - 4 31 y - = -1 2a(x-a);y= a 2 + \$ ; a = \$ 33 (\$)(1000) = 10 at x = 10 hours 55 a = 2 4 1 57 1.01004512; 1 + 10(.001) = 1.01 39 (2 + AX)^ - (8 + 6Ax) = AX)' + AX)^ 4 1 xl = i; x2 = - 40 43T=8sec;f(T)=96meters 45a>tmeters/sec2 Section 2.4 The Derivative of the Sine and Cosine (page 70) 1 (a) and (b) 3 0; 1; 5; \$ 5 sin(x + 2s); (sin h)/h -t 1; 2 s 7 cos2 B w 1 - 8 ' + f B4; f B4 is small 9 s i n i B m i B 11:;4 13PS=sinh;areaOPR=isinh<curvedareaih 1 5 c o s x = l - d - + L - . . . 1 7 &(cos(x+ h) - cos(x - h)) = ;(-sinxsinh) -+ -sinx 2.1 4.3.2.1 1 9 3 / = c o s x - s i n x = O a t x = q + n s 2 l ( t a n h ) / h = s i n h / h c o s h < ~ - + l -1. 2 , 2 , n o 25y=2cosx+sinx;y"=-y 2 7 y = - ~ c o s 3 x ; y = ~ s i n 3 x 2 3 S l o p e ~ c o s ~ x = ~ , 0 , 1. 29 In degrees (sin h)/h -+ 2x1360 = .01745 31 2 sin x cos x + 2 cos x(- sin x) = 0 Section 2.5 The Product and Quotient and Power Rules (page 77) 1 22 5&-* 5 (2 - 2)(x - 3) + (2 - 1)(x - 3) + (x - 1)(x - 2) 7 - ~ ~ s i n ~ + 4 x c o s x + 2 s i n x 9 2 x - 1 - ~ 1 1 2 ~ s i n x c o s x + ~ x - 1 / 2 s i n 2 x + ~ ( s i n x ) - 1 / 2 c o s ~
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