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222-unknown-06fafin-v1 - MATH 222 Lec 3 FINAL EXAM YOUR...

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Unformatted text preview: MATH. 222, Lec. 3, FINAL EXAM YOUR NAME T.A.'s NAME Show all your work. No calculators or references. 6. (20 pts) 7. (20 pts) 2. Evaluate 7774 .3 x tan-1(x) dx 0 3. Find dX x(x2 - 2x —» 3) 4. Evaluate the integral or show that it diverges 2 xdx (x-1)3 0 Decide whether the following series converge or diverge. Justify your answer. a) (a) Z21: l1(+1 k=1 ‘ or) (b) , k k(|n(k))2 k=2 Decide whether the following series are absolutely convergent, conditionally convergent, or divergent. Justify your answer. a) (a) E (-1 )n12n) (3n - 4) n=1 6?) \\ 7. Find all terms of the Maclaurin series expansion of the function f(x) = 1/(x2 + 16). What is the domain of convergence for the series. Justify your answer. 8. Find the solution of Y" — Y = sin(x) + x which satisfies the conditions Y(0) = Y'(0) = 0. 9. Sketch the curve r = 2 + Zcos( e. ) and find the area of the region bounded by it. /0 10. Find the unit tangent, principle normal, binormal, and curvature for the curve fit) = cosh(t)’i‘+ sinh(t)’j‘+ t/k\ an = o. // ...
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