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Calculus Solutions 11 - A-10 Answers to Odd-Numbered...

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A-10 Answers to Odd-Numbered Problems Section 6.4 Logarithms (page 258) 1 $ 3 - 1 5 lnx 7 ~ 0 8 5 = x(ln x)a s i n s x 9 11 $ l n t + C I 3 in$ 1 5 i l n 5 17-ln(ln2) 191n(sinx)+C 21-$ln(cos3x)+C 2 3 $ ( l n ~ ) ~ + C 27 in y = $ ln(x2 + 1); 2 = 29 * = esin cos x dFE dx 3 1 2 = exee' 33 l n y = e x l n x ; ~ = y e x ( l n x + ~ ) 5 5 l n y = - 1 s o y = : , z = O 3 7 0 39 -1 4 1 sec x 4 7 .l; .095; .095310179 4 9 -.01; -.01005; -.010050335 5 1 lYHSpital: 1 53 1 5 5 3 - 2 in 2 57 Rectangular area i + . . + < $ : $ = Inn In b 59Maximumate 6 1 0 6310gloeor& 6 5 1 - x ; l + x l n 2 (t+2)a -+ y = 1 - 1 never equals 1 67 Raction is y = 1 when ln(T + 2) - In 2 = 1 or T = 2e - 2 69 y' = -2- t+2 7 1 lnp = xln2;LD 2"ln2;ED p = eZLn2,p' = In2 esln2 75 24 = 42; yln x = xln y -+ '"2 = decreases after x = e, and the only integers before e are 1 and 2. y ' s Section 6.5 Separable Equations Including the Logistic Equation (page 266) I 7et - 5 3 ($x2 + 1)lI3 5 x 7 e l - ~ ~ ~ t 9 (?+&)a 11 y, =O;t = 1 YO 1 5 z = l + e - t , y is in 1 3 1 7 ct = ln3,ct = ln9 19 b = c = 13 . y, = 13 . lo6; at y = & (10) gives ln = ct + In c_'::,b so t = 1900 + = 2091 2 1 # dips down and up (avalley) 2 3 sc = 1 = sbr so s = $ , r = 25 Y = l+e-NY(N-l) ; ~=!d!!$l-+o 27 Dividing cy by y + K > 1 slows down y' 29 dR = CK dy ( y + ~ ) f > 09 * -+ 3 1
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