Pre-Calc Homework Solutions 450

Pre-Calc Homework Solutions 450 - 450 Cumulative Review dr...

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Unformatted text preview: 450 Cumulative Review dr dt dv dt 107. (a) Using the Ratio Test, lim n 112. (a) v(t) 2) 1 n 1 ( cos t)i (sin t)i (1 (cos t)j sin t)j a n 1 an lim n (x n n (x 2)n x 1 x 2 , which 2 1, a(t) means that the series converges for or 3 x 1. Furthermore, at x (b) Using NINT, the distance traveled is 3 /2 3 /2 3, the series v(t) dt /2 3 /2 /2 ( cos t)2 4. (1 sin t)2 dt is n 1 n 1 1 , which diverges, and at x 1, the series is n ( 1)n , which converges. The interval of n 2 /2 2 sin t dt 113. Yes. The path of the ball is given by x y 100(cos 45 )t 16t 2 50 2t and 16t 2 13 5 2 13 5 2 convergence is convergence is 1. (b) 3 x 1 1 (c) At x 3 x 1 and the radius of 100(sin 45 )t 130, we have t 13 2 50 2t. When x an 1 an n ln2 n xn and so 75.92 ft, high enough 108. (a) Using the Ratio Test, lim n y 16 5 50 2 2 lim n (n (n xn 1 1)ln2 (n nx ln 2 (n) 1) ln 2 (n n n 1 to easily clear the 35-ft tree. 114. Since r cos x, r sin y, the Cartesian equation is x y 2. The graph is a line with slope 1 and y-intercept 2. x , which means x 1. At x 1, 115. 1) 1) lim n x lim n 2 ln n 1) n ln (n lim that the series converges for 1 the series converges by the Integral Test: 1 dx x(ln x)2 b lim b 2 2 lim b 1 ln b 1 ln 2 1 dx x(ln x)2 1 ln 2 1 ln x b 2 [ 3, 3] by [ 0.5, 3.5] The shortest possible -interval has length 2 . 116. x r cos cos cos 2 , . So the x 1 and the radius of convergence interval is convergence is 1. (b) 1 x 1 (c) Nowhere 109. 1 22 ( 3)2 3 1 y dy dx r sin dy/d dx/d dy : d sin cos sin sin cos sin 2 cos 2 2 sin cos 2, 3 2 13 , 3 13 Zeros of cos cos (2 cos 110. 1 cos , 1 sin 3 1 3 , 2 2 sin 2 1 cos 2 2 cos2 0 1) 4 , or 3 0 1)(cos 2 , 3 dx : d 0 2 111. dy dx t 3 /4 dy/dt dx/dt t 3 /4 1 32 42 3 sin t 4 cos t t 3 /4 4 3 , and 5 5 4 and 5 3 . The 4 0, Zeros of sin tangent vectors are 4, 3 2 sin 0 or cos cos 1 2 3 0 4 , 5 3 3 . The normal vectors are , 5 5 3 4 , . 5 5 sin 0, , or 5 , 3 2 ...
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This note was uploaded on 10/05/2011 for the course MAC 1147 taught by Professor German during the Spring '08 term at University of Florida.

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