Pre-Calc Homework Solutions 344

Pre-Calc Homework Solutions 344 - 344 Section 8.4 c 0 c 56....

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Unformatted text preview: 344 Section 8.4 c 0 c 56. continued (b) Evaluate x e u xn du nx n 1 x e f (n n x n x (b) dx using integration by parts dv e x dx v e x n x f (x) dx 0 f (x) dx 0 f (x) dx f (x) dx 0 f (x) dx c c f (x) dx Thus, dx x e x ne 0 nx n 1 e x dx c f (x) dx c 0 f (x) dx c 0 1) x dx x b 0 0 c f (x) dx 0 f (x) dx c f (x) dx 0 f (x) dx lim b x ne bn eb nx n 1e x n 1e 0 x dx 0 f (x) dx 0 0 f (x) dx, because c c lim b n x dx f (x) dx 0 c f (x) dx 0 f (x) dx 0 f (x) dx 0. nf (n) Note: apply L'Hpital's Rule n times to show that lim b s Section 8.4 Partial Fractions and Integral Tables (pp. 444453) Quick Review 8.4 1. Solving the first equation for B yields B 3A Substitute into the second equation. 2A 3( 3A 5) 7 2A 9A 15 7 11A 22 A 2 Substituting A 2 into B 3A 5 gives B solution is A 2, B 1. 5. bn eb 0. 1) n(n nf (n), 1) ... f (1) n!; thus 0. (c) Since f (n f (n n 0 1) x e x dx converges for all integers n 1. The 57. (a) On a grapher, plot NINT sin x , x, 0, x or create a table x of values. For large values of x, f (x) appears to approach approximately 1.57. (b) Yes, the integral appears to converge. 1 58. (a) dx 1 x 2 1 lim b b dx 1 1 x2 1 lim b tan x b lim (tan b 1 1 tan 1 b) 4 dx 1 2 b 1 3 4 dx 1 1 1 x 2 lim b x2 b lim tan b x 1 lim [tan b 1 b tan 1 1] 2 dx 1 x2 3 4 4 4 4 2. Solve by Gaussian elimination. Multiply first equation by 3 and add to second equation. Multiply first equation by 1 and add to third equation. A 2B C 0 7B 5C 1 B 2C 4 Multiply third equation by 7 and add to second equation. A 2B C 0 9C 27 B 2C 4 Solve the second equation for C to get C 3. Solve for B by substituting C 3 into the third equation. B 2(3) 4 B 2 B 2 Solve for A by substituting B 2 and C 3 into the first equation. A 2(2) 3 0 A 1 0 A 1 The solution is A 1, B 2, C 3. 2x 1 3. x 2 3x 4 2x 3 5x 2 10x 7 2x 3 6x 2 8x x2 2x 7 x2 3x 4 x 3 2x 1 x x2 3 3x 4 ...
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