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Unformatted text preview: y = √ 1 + e x , 0 ≤ x ≤ 1 about the xaxis. (6) Sketch the curve (an ellipse) given by parametric equations x = 3 cos θ , y = 2 sin θ (0 ≤ θ ≤ 2 π ) by plotting points. Indicate with an arrow the direction in which the curve is traced as θ increases from 0 to 2 π . Find the equation of the tangent to the ellipse at the point where θ = π/ 4. Calculate the area of the ellipse. (7) In each case, determine whether the sequence converges, and if so ﬁnd the limit. (a) a n = n + (1) n n 2 n 2n . (b) b n = n + (1) n √ n √ nn . (8) (a) Does the series ∞ X n =1 n n 2 + 1 converge or diverge? (b) Show that the series ∞ X n =0 (3n(2)n ) converges, and ﬁnd its sum....
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This note was uploaded on 01/11/2010 for the course MATH 115 at Yale.
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 Math

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