LBS_119_Review_Sheet_BRIEF_ANSWERS_Exam__2

LBS_119_Review_Sheet_BRIEF_ANSWERS_Exam__2 - Copy #1...

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Unformatted text preview: Copy #1 PRACTICE EXAM 2 1. ANSWERS b) interval: a) interval: ( 1, 2 ) ( -e ,+ ) [ 0, 2/3] center = 3 / 2, radius = 1/ 2 interval: center = 1/ 3, radius = 1/ 3 interval: converges only at center x=0. center = 0, radius = 0 c) 2. center = 0, radius = d) You only need to show out to the THIRD POWER. I might have shown more than that so you can check your answers easier. a) e f (x) = x2 - x3 + x4 x5 - 2 6 e b) f (x) = x - n 2 3 x 3 3. a) n =0 ( -3 ) ( 2 x ) n n x - 2 ) + 2 -3( x - 2) ( b) 1 8 2 n =0 n e c) ( -x ) n =0 e - x ) ( n =0 d) n =0 ( -1) n n(n - 1)x n -2 4. 1 1 1 1 1 1 - + - + - = .448 a) 1 416 4 722 4 4 4 4 3 { 2 4 4 256 800 2304 Add these error term x 2 3x 4 1 + + ... 1 = b) lim + xe 0 40 6 c) 2.3 is outside the interval of convergence! We can't use it to approx ln 2.3. d) - 2 2 e) e4 Copy #2 PRACTICE EXAM 2 1. Converges only at center x=4. 2. [-5, - 1) 3. You only need to show out to the FOURTH POWER. I may have shown more terms here so you can check your answers easier. a) f ( x) = 1 + 2 x 2 + 2 x 4 + n 4 6 x 3 b) 1 1 f ( x) = 6 + x - x3 - x 4 3 6 c) 26 7 4. a) - 2 7( x + 3) 10 26 13 n= . b) n -1 - 7n 2 n( x + 3) 10 26n 13 n= 5. a) - 2 2 b) -27 2 -27 243 729 (.1) + (.1)3 - (.1)5 = -1.34798 c) 124 44 2 120 4 2800 43 4 4 3 14 2 Add these error term Copy #3 PRACTICE EXAM 2 1. 3. [-1,5) 2. Converges only at center x = -3 You only need to show out to the FOURTH POWER. I may have shown more terms here so you can check your answers easier. a) f ( x) = 1 + 3x 2 + . 9 4 9 6 x + x 2 2 n b) f ( x) = 3 + 5x - 5 2 5 3 5 4 x + x + x 2 3 4 c) 7 2 4. a) - 3 2( x + 3) 10 7 14 n= n -1 - 2n 3 n( x + 3) b) 1 14 7n n =0 5. a) -1 2 b) 6 c) 2 1 6(.1) - 2(.1) 2 + (.1)3 - (.1) 4 = 0.5806 3 5 1 4 4 4 2 4 4 43 123 Add these error term Copy #4 PRACTICE EXAM 2 1. 3. Converges only at center x = 3 2. (-2, - 1] You only need to show out to the THIRD POWER. I may have shown more terms here so you can check your answers easier. 1 1 a) f ( x) = x 2 - x 3 + x 4 2 3 b) 1 f ( x) = x + x3 3 c) 12 5 4. a) - 1 5( x + 2) 10 4 12 n= . n n -1 - n 1 5 n( x + 2) b) 1 4 12n n =0 5. a) 3 2 b) -14 62 2 + x 3 15 c) -14 3 ...
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