Written Ass1 Math262 Fall09

Written Ass1 Math262 Fall09 - 1 1 ( 1) 2 ( 3) n n n n x n-...

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Written Ass.1 Math 262 Fall 09 1. Does the series 1 1 (1 ) ! n n n n = + converge (absolutely or conditionally) or diverge. Justify your answer. 2. For which values of x does the series 0 ! n n x n = converge (absolutely or conditionally) or diverge. Justify your answer. Do not forget to analyse the endpoints. 3. For which values of x does the series 3 4 ( 2) 3 n n n x n = - - converge (absolutely or conditionally) or diverge. Justify your answer. Do not forget to test the end points. 4. Find the first four terms in the Maclaurin series expansion of 1 3 (1 2 ) x + and an expression for the remainder after these first four terms. 5. Find the radius of convergence of the power series
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Unformatted text preview: 1 1 ( 1) 2 ( 3) n n n n x n- =-- . Hence find the interval of convergence including the end points. 6. Find the Taylors series of f(x) = 1/x 2 in powers of x + 1. 7. Find the Maclaurin series for E(x) = 2 1 x t e dt t-- and use it to evaluate E(.1) with an error 3 10- . 8 Evaluate 0.4 4 4 1 ( 10 ) x dx error-+ < 9 Find the equation of the plane passing through the line x + y = 2, y - z = 3 and perpendicular to the plane 2x + 3y + 4z = 5. 10 Show that the line 3 1 2 2 4 y z x +-- = = is parallel to the plane 2y z = 1. What is the distance between the line and the plane?...
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