Calculus Solutions 9

Calculus Solutions 9 - A-8 Answers to Odd-Numbered Problems...

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A-8 Answers to Odd-Numbered Problems Section 5.6 Properties of the Integral and Average Value (page 212) 1~=~~~~x~dx=~e~ualsc~atc=f(~)~~~ ~~=~J~cos~xdx=~e~ualscos~catc=~and$ 2dz 6ir=/12=~equals$atc=fi 7J:v(x)dx gFalse,takev(x)<O 11The; 3 J', v(x)dx + $ . J: v (x)dx = i J,S 13 False; when v(x) = z2 the function x2 - i is even 15 False; take v(x) = 1; faetor ? is missing 17 = A Ja v(x)dx 19 0 and ? b-a 21 v(x) = Cx2; v(x) = C. This is 'constant elasticity" in economics (Section 2.2) 23 V + 0; + 1 25 iJi(a-x)dx= a+ 1ifa > 2;;s; la- xldx= ? area = $ -a+ < 2; distance = absolute value 27 Small interval where y = sin B has probability $; the average y is = 2 A 29 Area under cos 0 is 1. Rectangle 0 < 0 5 5,O 5 y 5 1has area 5. Chance of falling across a crack is $ = 1. %dt = -220- gsin % = Vave 31 $, &,. .., 10.5 33 5 J,'~~ocos 35 Any V(X) = veve,(x) odd(^); (X + = (3x2 + 1) + (x3 + 3%); ;)i = - & 31 16 per class; E(X) = 64 = 22.9 39 F; F; T; T 8 Section 5.7 The Fundamental Theorem and Its Applications (page 219) 1cos2 x SO S(X~)~(~X)=~X~ ~v(x+I)-V(X) gem- 2. sin2 t dt ll/;v(u)du 130 152sinx2 17u(x)v(x) 19th-'(sinx)cosx=xcosx 21 F; F; F; T 23 Taking derivatives v(x)
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