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MATH 101 Quiz #4 (v.T3) Last Name: Thursday, March 3 First Name: Grade: Student-No: Section: Very short answer question Z ∞ 1. 1 mark What is the largest value of q for which the integral 1 1 dx diverges? x5q Answer: Short answer questions—you must show your work 2. 2 marks The total error using the trapezoid rule to integrate f (x) over [a, b] is bounded by M (b − a)3 /(12n2 ), where |f 00 (x)| ≤ M for all a ≤ x ≤ b. R1 If the integral −2 2x4 dx is approximated using the trapezoid rule with 90 subintervals, what is the largest possible error between the approximation T90 and the true value of the integral? Show your work, but you may leave your answer in calculator-ready form. Z 3. 2 marks Evaluate (x2 1 dx. + 25)3/2 Long answer question—you must show your work 4. 5 marks Evaluate the following indefinite integral using partial fractions: Z 3x2 − 4 F (x) = dx. (x − 2)(x2 + 4)