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222-dickey-07fafin

222-dickey-07fafin - MATH 222 Lee 3 Final Exam YOUR NAME...

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Unformatted text preview: MATH 222, Lee. 3, Final Exam YOUR NAME T.A.'s NAME Show all your work. No calculators or references. 1.(2o points) 2.(20 points) .3.(20 points) 4.(2o points) 5.(20 point-s) 6 (20 pomts) - Z. 1. Evaluate the the following integrals (a) g x3|n(x)-dx 2 / (b) .___\$_____ g (X +1)(X + 2)2 / Decide whether each of the: following integrals is convergent or divergent. If the integralis divergent justify your answer. If the integral is convergent evaluate it. a? (a) _.Mxﬂ2_dx (b) (1 + e-X) dx 1 — x2 x O / 3. Decide whether the following series converge of diverge. Justify your answer. a) w (a) E In n (b) (-1)n+1 n , n2 5n + 1 M:-/ m:/ 4. Find the Taylor series expansion for 1/(2 + x)3 about x = 0. What is the interval of convergence for the series? 5. Solve the following initial value problems-.- (a) Y' + x2Y = x2, Y(0) = O (b) Y" + 2Y' + Y = cos(x) + x, Y(O) = 0, Y'(O) = 0. ﬁx 6. '(a) Find the area of the region enclosed by one Icop of r = cos(36’ ). (b) Find the length of r = 5cos( 9) if 0 _<_ 9 _<_ 37Z/4. \| 7. (a) Find the equation of the line passingghrough the point (1,2,3) and parallel to the vector V: 3 I- j + 4 k (b) Find the equation of the plane containing the 3 points (1,11,), (1,2,1), (21.3) 8. (a) Find the area of the triangle with vertices (1,2,3), (1 ,-1 ,4), (2,1 ,1.) (b) Find the yolgme of thggaralieipiped determined byA thevectorsU=i+j+k, V=i+2j+1<, W=i+j+3k 9. Find the unit tangent, principleA normal, and curvature for r (t): etcos(t)' I + etsin(t)/‘ ] + et'A k /a> 10. Find the tangential and/\normtal componentsvof the acceleration if ﬁt) = t i + t2 J + t2 k. ‘ // ...
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222-dickey-07fafin - MATH 222 Lee 3 Final Exam YOUR NAME...

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