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MATH 101 Quiz #1 (v.M1) Last Name: Friday, January 15 First Name: Grade: Student-No: Section: Very short answer question R5 1. 1 mark Estimate 1 x3 dx using three approximating rectangles and left hand end points. Please write your answer in the box. A “calculator-ready” answer is acceptable. Answer: Short answer questions—you must show your work 2. 2 marks A car’s brakes are applied at t = 0 seconds and the car decelerates continuously until it comes to a stop at t = 2 seconds. The car’s speed at half-second intervals is given in the table below. Find the best possible lower estimate for the distance that the car traveled during these two seconds. A “calculator-ready” answer is acceptable. t (s) 0 0.5 1.0 1.5 2 v (m/s) 40 30 24 10 0 3. 2 marks The functions f (x) and g(x) obey Z Find 1 f (x) dx = 1 0 R2 ⇥ 1 3f (x) Z 2 f (x) dx = 2 0 Z 0 g(x) dx = 3 1 Z ⇤ g(x) dx. A “calculator-ready” answer is acceptable. 2 g(x) dx = 4 0 Long answer question—you must show your work 4. 5 marks (a) Express as a definite integal. n X 4 lim n!1 n i=1 (b) Evaluate the integral of part (a). s 4 ✓ 4i 2+ n ◆2