Calculus Solutions 16

Calculus Solutions 16 - Answers t o Odd-Numbered Problems 1...

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$; Answers to Odd-Numbered Problems 9 p= 1.1+;.2+ . ..+1.7 =4 11 $* 2xdx = I ln(1 + x2)]F = +m 7 7 o n(l+x3) m ~xe-~"dz = [-xe-""]F + e-axdx = a 2dx = Z tan-' x. JX e-"dx = 1 - e-X. ae-aXdx = 1 - e-ax 17 $= Le-x/10dZ = -e-~/10 w 1 JX 0 I" n(l+x3) rr 0 0 10 10 I10 = ; Exponential better than Poisson: 60 years --+ .01e-.~" dx = 1 - e-s6 = .45 y = 7; three areas = $ each because p - o to p is the same as p to p + o and areas add to 1 -2p J xp(x)dx + p2 J p(x)dx = -2p . p + e = -pa l p=o.$+1.$+2.+1; 02=(o-1)2.$+(1-1)2.$+(2-1)2.$=Z 3 ' Al~oxn~~,-p~=O.$+1.1+4.~-1=Z 3 3 00 ~e-*/~dx - - 2; 1 - Jo 7 p = -7 4 e-s72dx = 1 + [e-x/2]: = e-2 Standard deviation (yes - no poll) 5 1 = = & Poll showed = % peaceful. 2n 95% confidence interval is from % - & to + &, or 93% to 100% peaceful. 31 95% confidence of unfair if more than $ = & = 2% away from 50% heads. 2% of 2500 = 50. So unfair if more than 1300 or less than 1200. 33 55 is 1.50 below the mean, and the area up to p - 1.50 is about 8% so 24 students fail. A grade of 57 is 1.30 below the mean and the area up to p - 1.30 is about 10%. 35 .999; .9991°00 = (1 - &)loo' = $ because - i)" 4 $. Section 8.5 Masses and Moments
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