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MAth242Final06

# MAth242Final06 - 7 Show that the parametric curve x = t 2 y...

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MATH 242, Fall 2006 Final Exam: December 15, 8:00-10:00 Only the answer books will be graded. Please write your name and section number on the cover. Please circle final answers and cross out incorrect work. You must justify all answers to receive full credit. You may not use calculators, notes, or any other kinds of aids. Each question is worth 10 points. 1. In 1990, twenty wolves were introduced into a large wilderness area that has essen- tially unlimited food. In 1998, the wolf population had increased to 80. What will the wolf population be in 2010? 2. Simplify the expression sin - 1 sin 3 π 2 . 3. Find a cartesian representation of the polar curve r = 4 sin θ , and identify the curve. 4. Find the derivative of e sinh ( 5 x ) at x = 0. 5. Evaluate 2 x 1 + 2 x dx . 6. Evaluate, or show the divergence of, 1 ds
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Unformatted text preview: ) . 7. Show that the parametric curve x = t 2 , y = t 3-4 t has two tangent lines at the point ( 4, 0 ) , and ﬁnd equations for both lines. 8. Find the value (sum) of the series ∞ ∑ n = 1 1 3 2 n-1 . 9. Find the Taylor polynomial T 2 ( x ) at a =-1 for the function x 3 . 10. Find lim x → e 4 x-1-4 x x 2 . d dx ( sin-1 x ) = 1 √ 1-x 2 d dx ( tan-1 x ) = 1 1 + x 2 1-sin 2 θ = cos 2 θ 1 + tan 2 θ = sec 2 θ sin 2 θ = 1 2 ( 1-cos 2 θ ) cos 2 θ = 1 2 ( 1 + cos 2 θ ) Logistic equation: dP dt = kP ³ 1-P K ´ , P ( t ) = K 1 + Ae-kt , A = K-P P θ π 6 π 4 π 3 π 2 2 π 3 3 π 4 5 π 6 π cos θ 1 √ 3 2 1 √ 2 1 2-1 2-1 √ 2-√ 3 2-1 sin θ 1 2 1 √ 2 √ 3 2 1 √ 3 2 1 √ 2 1 2...
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