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