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MATH 101 Quiz #1 (v.A1) Last Name: Friday, January 15 First Name: Grade: Student-No: Section: Very short answer question 1. 1 mark Let f be a function on the whole real line. Express Z 7 f (x) dx as a limit of Riemann 1 sums, using the right endpoints. Write your answer in the box. Answer: Short answer questions—you must show your work 2. 4 marks Each part is worth 2 marks. p R3 (a) Evaluate 3 2 + 9 x2 dx. Simplify your answer completely. Answer: n X 2 e n!1 n i=1 (b) Express lim i/n cos(2i/n) as a definite integral. Write your answer in the box. Answer: Long answer question—you must show your work Z 3 (x + x3 ) dx using the definition of the definite integral. You may use the 0 P P 2 4 3 2 summation formulas ni=1 i = n 2+n and ni=1 i3 = n +2n4 +n . You may leave your answer in “calculator-ready” form. (No credit will be given for using integration rules, but you may use them to check your answer.) 3. 5 marks Find