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Unformatted text preview: . Hint: ∞ X n =0 3 n x n is a geometric series with ratio r = 3 x . What does it converge to? Math 166 Final Exam Page 5 6. Taylor’s Formula with remainder applied to f ( x ) = ln(2 + 3 x ), at the centering point a = 0, shows that ln(2 + 3 x ) = P 2 ( x ) + R 2 ( x ), where P 2 ( x ) is the Maclaurin polynomial of degree 2 and R 2 ( x ) is the remainder term. Determine P 2 ( x ) and R 2 ( x ) in this case. Math 166 Final Exam Page 6 7. Find the tangent line to the parametric curve x = t 3 + t , y = t 21, 0 < t < 2, at the point (2 , 0). Hint: The curve passes through the point (2 , 0) when t = 1. 8. Find the area of one leaf of the 3leaved rose r = 5 sin 3 θ . (Recall the trigonometric identities: cos 2 x = 1 2 (1 + cos 2 x ), sin 2 = 1 2 (1cos 2 x ), and sin 2 x = 2 sin x cos x .)...
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 Spring '08
 Hotlz
 Math, Calculus, Taylor Series, Mathematical analysis

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