Hw10 - good is your approximation at x = 1 1 10.5 Find the Cartesian equation of the curve which is given by a parametric equation x = 2 cos θ y =

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CALCULUS 1501 WINTER 2010 HOMEWORK ASSIGNMENT 10. Due April 5. 10.1. Find the Maclaurin series for f ( x ). Find the radius of convergence of the series, and show, using Lagrange’s remainder theorem that the series converges to f ( x ). (i) f ( x ) = xe 2 x . (ii) f ( x ) = sin x 2 . 10.2. Find the first 3 terms of the Taylor series of f ( x ) centred at a : (i) f ( x ) = sec x at a = π 4 . (ii) f ( x ) = tan - 1 x at a = 1. 10.3. Find the Maclaurin series for f ( x ) = x 2 1 + x . 10.4. Approximate the function f ( x ) = x x at a = 1 by a Taylor polynomial of degree 2. How
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Unformatted text preview: good is your approximation at x = 1 . 1? 10.5. Find the Cartesian equation of the curve which is given by a parametric equation x = 2 cos θ, y = 3 sin θ, θ ∈ (-π,π ) . Sketch the curve indicating with an arrow the direction in which the curve is traced as the parameter increases. 10.6. Evaluate the integral Z 1 ln(1-x ) x dx. Hint: Use Taylor series expansion and the identity ∑ ∞ n =1 1 n 2 = π 2 6 . 1...
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This note was uploaded on 07/15/2010 for the course MATH 1501 taught by Professor Shafikov during the Winter '10 term at UWO.

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