MATH 101 Quiz #1 (v.M2)
Last Name: First Name:
Friday, January 15
Student-No:
Grade:
Section:
Very short answer question
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:
Short answer questions—you must show your work
2. 2 marks A car’s gas pedal is applied at t = 0 seconds and the car accelerates continuously until t = 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) 0 0 .
5 1 .
0 1 .
5 2 v (m/s) 0 14 22 30 40
3. 2 marks The functions f ( x ) and g ( x ) obey
Z
1
Z
2
Z
0 f ( x ) dx = 1 f ( x ) dx = 2 g ( x ) dx = 3
Find
0 0 1
R
2
1
⇥
3 g ( x ) 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
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