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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 tan1(x) dx
0 3. Find dX
x(x2  2x —» 3) 4. Evaluate the integral or show that it diverges
2 xdx
(x1)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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 Fall '08
 Wilson
 Calculus, Maclaurin, Maclaurin Series expansion

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