Mock Gateway 4 Answers

Mock Gateway 4 Answers - 3-= 3 8. 3 = e ln 3 3 x = e (ln 3)...

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Answers to Mock Gateway IV 1. f ( x ) = e x + cos x + C f (0) = 2 + C C = - 1 f ( x ) = e x + cos x - 1 2. s 0 ( t ) = - t + C s 0 (0) = C C = 3 s 0 ( t ) = - t + 3 s ( t ) = - 1 2 t 2 + 3 t + D s (0) = D D = 7 s ( t ) = - 1 2 t 2 + 3 t + 7 3. Z 1 0 ( x 2 - 2 x + 2) dx = 1 3 x 3 - x 2 + 2 x ± ± 1 0 = ² 1 3 (1) 3 - (1) 2 + 2(1) ³ - ² 1 3 (0) 3 - (0) 2 + 2(0) ³ = 4 3 4. Z ´ 1 x 2 - x + 2 x µ dx = Z ( x - 2 - x 1 / 2 + 2 x - 1 / 2 ) dx = x - 1 - 2 3 x 3 / 2 + 4 x 1 / 2 + C
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5. Z e 1 ± 3 x ² dx = 3 Z e 1 ± 1 x ² dx = 3 ln x ³ ³ e 1 = 3 ln e - 3 ln 1 = 3 6. Z π/ 2 0 2 cos θdθ = 2 sin θ ³ ³ π/ 2 0 = 2 sin π/ 2 - 2 sin 0 = 2 7. . (a) Z 1 x 2 + 1 dx = Tan - 1 x + C (b) Z 3 / 2 0 1 1 - x 2 dx = Sin - 1 x ³ ³ 3 / 2 0 = Sin - 1 3 / 2 - Sin - 1 0 =
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Unformatted text preview: 3-= 3 8. 3 = e ln 3 3 x = e (ln 3) x Z 3 x dx = Z e (ln 3) x dx Substitute u = (ln 3) x . Then du = (ln 3) dx and we get Z e u 1 ln 3 du = e u ln 3 + C = e (ln 3) x ln 3 + C = 3 x ln 3 + C 9. F ( x ) = e-x 2...
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This note was uploaded on 05/15/2008 for the course MATH 231 taught by Professor Mooney during the Spring '08 term at Wisconsin Milwaukee.

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Mock Gateway 4 Answers - 3-= 3 8. 3 = e ln 3 3 x = e (ln 3)...

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