# extenssion

Education

19

All Questions

15

Multiple Choice

0

True False

4

Essay

0

Short Answer

0

Not Answered

Q 1

Which of the following expressions gives the area of region R?
A)
B)
C)
D)

Free

Multiple Choice

C

Q 2

Which of the following expressions gives the volume when region R is rotated about the line ?
A)
B)
C)
D)

Free

Multiple Choice

C

Q 3

For problems 3 and 4,region Q is bounded by , , and .
-What is the area of region?
A)0
B)1.5
C)
D)3

Free

Multiple Choice

D

Q 4

Which of the following expressions gives the volume of a solid whose base in the xy-plane is region Q and whose cross sections,perpendicular to the x-axis,are squares with a side in the xy-plane?
A)
B)
C)
D)

Multiple Choice

Q 5

For Question 5,region W is bounded by , , ,and .
-What is the area of the region W?
A)12
B)
C)
D)

Multiple Choice

Q 6

In the closed interval ,if ,for what value of k does the region bounded by and the line have the same area as that bounded by and the x-axis?
A)
B)
C)
D)

Multiple Choice

Q 7

Air is being pumped into a spherical balloon at the rate of cm

^{3}/min,but there is a small hole in the balloon and at the same time air is leaking out at the rate of cm^{3}/min. Which of the following is true for ,where t is measured in minutes? A) represents the volume of the balloon after the first 10 minutes. B) represents the increase in volume each minute during the first 10 minutes. C) represents the increase in volume during the first 10 minutes. D) Multiple Choice

Q 8

The revenue and expenditures for a small company are analyzed and predicted for the next 5 years.The current annual revenue is $110,000 and growing at an annual rate of 30%,while the expenditures are modeled with a sinusoidal function.If and ,to the nearest dollar,what is the average annual profit for the company when the expenditures reach a maximum value on the interval ?
A)191,441
B)159,534
C)119,651
D)79,767

Multiple Choice

Q 9

Region G is bounded by the curve , ,and the x-axis.Order from smallest to largest the volumes determined when G is rotated about the axes:
I) II. III.
A)
B)
C)
D)

Multiple Choice

Q 10

The base of a solid is bounded by and in the xy-plane,as shown in the figure below.Each cross section perpendicular to the x-axis is a rectangle with one side in the xy-plane and whose height is 2.What is the volume of the solid?
A)3.121
B)4.454
C)6.243
D)12.486

Multiple Choice

Q 11

Find the combined area of the two regions bounded by the curves and as shown in the figure bellow.
A)0.073
B)0.203
C)0.276
D)0.828

Multiple Choice

Q 12

The velocity of a particle moving along a line is given by for the interval .
-How far to the right of the starting point will the particle be at ?
A)2.212
B)1.548
C)3.318
D)4.424

Multiple Choice

Q 13

What is the distance that the particle has traveled on this time interval?
A)2.212
B)6.596
C)9.234
D)13.191

Multiple Choice

Q 14

If the position of the particle at time is −1,then what is the position of the particle when it is farthest to the right on this time interval?
A)2.212
B)6.702
C)13.191
D)10.053

Multiple Choice

Q 15

Which of the following expressions represents the volume of the solid generated when the region bounded by and is rotated about the line ?
A)
B)
C)
D)

Multiple Choice

Q 16

Let f be the function given by as shown in the sketch below,where the region R is bounded by the graph of ,the y-axis,and the horizontal line .
-Find the area of the region R.

Essay

Q 17

A vertical line ,where is chosen so that the area of the region bounded by ,the y-axis,the horizontal line ,and the line is half the area of region R.What is the value of h?

Essay

Q 18

Find the volume of the solid formed when region R is rotated about the line .

Essay

Q 19

A horizontal line ,where k is greater than 4,is chosen so that the volume of the solid formed when region R is rotated about the line is twice the volume of the solid found in part (c).Set up,but do not evaluate,an integral expression in terms of a single independent variable which represents the volume of this solid.

Essay