FINAL

# FINAL - dy dx = 3 x 2 2 y 5. Find an equation of the...

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1. Evaluate the following integrals. (10 points each) (a) ± x sin xdx (b) ² 1 0 1 4 - x 2 dx 2
(c) ± 1 x 2 - 4 dx (d) ² x 2 e x 3 dx 3

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2. Determine whether the following integral is convergent or divergent. Evaluate if it is convergent. (10 points) ± 0 -∞ xe x dx 3. Find the area of the surface obtained by rotating the curve y = x 2 from (0 , 0) to (1 , 1) about the y - axis. (15 points) 4
4. Solve the diﬀerential equation. (10 points)

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Unformatted text preview: dy dx = 3 x 2 2 y 5. Find an equation of the tangent line to the curve x = t 2 + 3 t , y = 2 t-1 at t = 0 . (10 points) 5 6. Find the shaded region enclosed by r = 1 + cos θ and the horizontal axis. (15 points) 6 7. Find the exact length of the polar curve. (10 points) r = e θ , ≤ θ ≤ π 8. Test for convergence or divergence. (10 points each) (a) ∞ ± n =0 1 (-10) n 7 (b) ∞ ± n =1 n-1 2 n (c) ∞ ± n =1 n n 4 n (d) ∞ ± n =1 1 + sin n 5 n 8 9. Find the radius and interval of convergence. (15 points) ∞ ± n =1 (3 x-2) n n · 3 n 10. Find a power series representation for the given function and determine the interval of convergence. (10 points) f ( x ) = x x 2 + 1 9 11. Find the Taylor series for f ( x ) = x-x 2 centered at x = 1 . (10 points) 12. Find the Maclaurin series for f ( x ) = e x . Use your answer to evaluate ∞ ± n =0 1 n ! . (15 points) 10...
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## This note was uploaded on 02/25/2010 for the course MAC 2312 taught by Professor Zhang during the Spring '07 term at FSU.

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FINAL - dy dx = 3 x 2 2 y 5. Find an equation of the...

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