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MATH 101 Quiz #4 (v.A2) Last Name: Friday, March 4 First Name: Grade: Student-No: Section: Very short answer question 1 3x3 − 2x2 + 9 in the partial fraction expansion of 2 . x−1 x (x − 1)(x2 − 2x + 3) Simplify your answer completely. 1. 1 mark Find the coefficient of Answer: Short answer questions—you must show your work Z 2. 2 marks Evaluate (x2 1 dx. + 9)3/2 R1 3. 2 marks The integral −1 cos(x2 ) dx is estimated using the Midpoint Rule with 1000 points. Show that the error in this approximation is at most 2 · 10−6 in absolute value. Rb You may use the fact that when approximating a f (x) dx with the Midpoint Rule using n points, the absolute value of the error is at most K(b − a)3 /24n2 where |f 00 (x)| ≤ K for all x ∈ [a, b]. Long answer question—you must show your work 4. 5 marks Find the x-coordinate of the centre of mass of the (infinite) region lying to the right of the line x = 2, above the x-axis, and below the graph of y = 8/x3 .