26.Find the limit: AnswersA.

0

B.

1

C.

0.5

D.

1

Question27.Find the limit: AnswersA.

0

B.

1

C.

D.

1

Question28.Find the limit: AnswersA.

0

B.

C.

D.

Question29.Find the approximate area of the region bounded by the curvesy=x³-xandy= 3x.AnswersA.

7.0

B.

7.6

C.

3.8

D.

8.0

Question30.Find the approximate area of the region bounded by the curvesy= sec²xandy= 8 cosxon the interval.AnswersA.

17.32

B.

8.67

C.

9.86

D.

10.39

Question31.Find the approximate volume of the solid obtained by rotatingx= 2,x= 0,y= 9 about they-axis.AnswersA.

508.94

B.

610.22

C.

162.0

D.

324.1

Question32.Find the approximate volume of the solid obtained by rotating the region betweeny=x⁴,y= 0, andx= 1 about the linex= 2.AnswersA.

1.47

B.

0.47

C.

2.09

D.

0.67

Question33.Find the approximate length of the curvey= ln(secx), 0 x.AnswersA.

0.41

B.

0.88

C.

2.76

D.

0.58

Question34.Find the approximate area of the surface obtained by rotatingx=(y²+ 2)^3/2, 1 y 2 about thex-axis.AnswersA.

32.99

B.

10.5

C.

5.25

D.

16.49

Question35.An object is moving along the coordinate line with velocityv(t) = 5 cost, 0 x 2. What is the object's displacement during the interval fromt= 0 tot= 2?AnswersA.

10

B.

20

C.

5

D.

0

Question36.Which of the following gives the volume of the solid created by revolving a curvef(x) around they-axis?AnswersA.

V=

B.

V=

C.

V=

D.

V=

Question37.Given a solid whose cross-section is defined byA(x), the volume of the solid is given by ________.AnswersA.

V=

B.

V=

C.

V=

D.

none of these

Question38.Find the volume of the solid obtained by rotating the area bounded byy= sinxand thex-axis on the interval 0 x 2about thex-axis.AnswersA.

5.490

B.

2.754

C.

10.912

D.

9.870

Question39.A solid has a flat base, which is bounded by the graph ofy=x³andy=in the first quadrant only. Each cross section of the solid perpendicular to thex-axis is the shape of a square. Find the volume of this solid.AnswersA.

B.

C.

D.

Question40.A tank is formed by revolving the graph of y=x⁴around they-axis. The tank has a height of 16. Find the value ofmsuch that the liney = mrepresents the height at which the tank is half full. Round your answer to three decimal places.AnswersA.

16.549

B.

15.410

C.

10.079

D.

6.105

Question41.If an object is displaced a distancedby a constant forceF, the amount of work done is given by which equation?AnswersA.

W=F+d

B.

W=F-d

C.

W=Fd

D.

W=F/d

Question42.If the force acting on an object is given by the functionF(x), then the work done on the object fromx=atox=bis given by which of the following?AnswersA.

W=

B.

W=

C.

W= (b-a)

D.

W=

Question43.According to Hooke's Law, the force needed to displace a springxunits from its natural length is given by which equation?AnswersA.

F(x) =x+k

B.

F(x) =k^x

C.

F(x) =kx

D.

F(x) =kx²

Question44.Suppose that a force of 20Nstretches a spring 0.4 m beyond its natural length. How far will a 40Nforce stretch the spring?AnswersA.

1.0

B.

0.4

C.

0.2

D.

0.8

Question45.A cylindrical tank of about 8 m high, with a radius of 3 m, is filled half way with water. Approximately how much work is needed to pump the water to the rim of the tank?AnswersA.

6.650 x 10⁶Nm

B.

8.867 x 10⁶Nm

C.

6.788 x 10⁶Nm

D.

2.217 x 10⁶Nm

E.

none of these

Question46.Consider the region,R, bounded by thex-axis, they-axis, and the graphs of the equationsy=andy= lnx. Find the area of the regionR.AnswersA.

5.497

B.

1.483

C.

0.879

D.

0.013

Question47.Consider the region,R, bounded by they-axis and the curvey=x⁵for 0 x 3. A tank is formed by rotatingRabout they-axis. Find a function,V(h), that gives the volume of water in the tank at any vertical height,h, wherehis measured in feet from thex-axis.AnswersA.

V(h) =

B.

V(h) =

C.

V(h) =

D.

V(h) =

Question48.Consider the region,R, bounded by they-axis and the curvey=x⁵for 0 x 3. A tank is formed by rotatingRabout they-axis. In question 47, you found the function,V(h). At what height is the water when the tank is 3/4 full?AnswersA.

58.904 feet

B.

150.931 feet

C.

197.863 feet

D.

200.653 feet

Question49.A cylindrical water tower 10 ft in diameter and 40 ft in height has its center 100 ft above the ground. A pump on the ground fills the tank with water whose density is 62.4 lb/ft³. How much work is done in filling the tank half way?AnswersA.

35.2 million ft-lb

B.

15.7 million ft-lb

C.

8.8 million ft-lb

D.

none of these

Question50.A cylindrical water tower 10 ft in diameter and 40 ft in height has its center 100 ft above the ground. A pump on the ground fills the tank with water whose density is 62.4 lb/ft³. How much work is done in filling the tank completely?AnswersA.

70.4 million ft-lb

B.

31.4 million ft-lb

C.

17.6 million ft-lb

D.

none of these

Dont need to show work :)