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MATH 101 Quiz #1 (v.M2) Last Name: First Name: Friday, January 15 Student-No: Grade: Section:

1. 1 mark Estimate R 3 3 x 2 dx using three approximating rectangles and left hand end points.

Please write your answer in the box. A “calculator-ready” answer is acceptable.

Answer:

2. 2 marks A car’s gas pedal is applied at until t t = 0 seconds and the car accelerates continuously = 2 seconds. The car’s speed at half-second intervals is given in the table below.

Find the best possible upper estimate for the distance that the car traveled during these two seconds. A “calculator-ready” answer is acceptable.

t (s) v (m/s) 0 0 0 .

5 14 1 .

0 22 1 .

5 30 2 40 3. 2 marks The functions f ( x ) and g ( x ) obey Find Z 1 Z 2 Z 0 R 2 1 ⇥ 0 3 g ( f ( x ) dx = 1 x ) f ( x ) dx = 2 g ( x ) dx = 3 0 1 f ( x ) ⇤ dx . A “calculator-ready” answer is acceptable.

Z 0 2 g ( x ) dx = 4

Long answer question—you must show your work 4. 5 marks (a) Express lim n !1

i =1 6 s 9 n as a definite integal.

(b) Evaluate the integral of part (a).

✓ 3 + 6 i ◆ 2 n Page 2