Unlock document.
This document is partially blurred.
Unlock all pages and 1 million more documents.
Get Access
Stewart_Calc_7ET ch05sec01
MULTIPLE CHOICE
1. Estimate to the hundredth the area from 1 to 5 under the graph of using four
approximating rectangles and right endpoints.
a.
b.
c.
d.
e.
f.
2. Approximate the area under the curve from using ten approximating
rectangles of equal widths and right endpoints. The choices are rounded to the nearest
hundredth.
a.
0.36
b.
0.02
c.
0.72
d.
0.98
e.
1.08
3. Determine a region whose area is equal to .
a.
b.
c.
d.
e.
NUMERIC RESPONSE
1. The speed of a runner increased steadily during the first three seconds of a race. Her speed
at half-second intervals is given in the table. Find a lower estimate for the distance that she
traveled during these three seconds.
2.8
3.5
6.9
8.2
12.2
16.3
2. By reading values from the given graph of , use five rectangles to find a lower estimate, to
the nearest whole number, for the area from 0 to 10 under the given graph of .
3. Approximate the area under the curve from 1 to 2 using ten approximating
rectangles of equal widths and right endpoints. Round the answer to the nearest hundredth.
4. The velocity graph of a braking car is shown. Use it to estimate to the nearest foot the
distance traveled by the car while the brakes are applied.Use a left sum with n = 7.
5. The velocity graph of a car accelerating from rest to a speed of 7 km/h over a period of 10
seconds is shown. Estimate to the nearest integer the distance traveled during this period.
Use a right sum with .
6. Find an expression for the area under the graph of as a limit. Do not evaluate the limit.
SHORT ANSWER
1. Use the definition of area to find the area of the region under the graph of f on [a, b] using
the indicated choice of ck.
= , [0, 2], ck is the left endpoint
2. Use the definition of area to find the area of the region under the graph of f on [a, b] using
the indicated choice of ck.
= + 6x + 1, [ , 1], ck is the right endpoint
