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1. given the curve that...

1. given the curve that is described by the equation r=3 cos theta, find the angle that the tangent line makes wit the radius vector when theta=120 degree.

a. 30 degree

b. 45 degree

c. 60 degree

d. 90 degree

15. a line rotates in a horizontal plane according to the equation theta=2t cube - 6t, where theta is the angular position of the rotating line, in radians and t is the time, in seconds. determine the angular acceleration when t=2 sec.

a. 6 radians per sec square

b. 12 radians per sec square

c. 18 radians per sec square

d. 24 radians per sec square

3. evaluate the anti derivative of cot 2x dx.

a. 1/2 Ln sin sx+c

b. 1/2 Ln cos 2x + c

c. 1/2 Ln sec 2x + c

d. 1/2 Ln csc 2x + c

2. evaluate the anti derivative of sin 4x cos square 4x dx.

a. cos cube 4x/3 + c

b. - cos cube 4x/3 + c

c. cos cube 4x/ 12 + c

d. - cos cube 4x/12 + c

3. evaluate the anti derivative of e the power of 3x dx.

a. e the power of 3x + c

b. 1/3 e the power of 3x + c

c. e the power of 4x +c

d. 1/4 e the power of 4x + c

4. which of the following is a step in evaluating the anti derivative of cos square 5x dx

a. the anti derivative of 1+cos 10x/2 dx

b. the anti derivative of 1-cos 10x/2 dx

c. the anti derivative of 1 + cos 10x/20 dx

d. the anti derivative of 1-cos10x/20 dx

5. to evaluate the anti derivative of 3x square cos(2x cube - 4) dx, it is necessary to let

a. u=3x square

b. u=6x

c. u=2x cube - 4

d. u= 6x square

6. evaluate the anti derivative of dx/the square root of 9-8x-x square

a. sin the power of -1(x+4)/5 + c

b. sin the power of -1(x-4)/5 +c

c. Ln the square root of 9-8x-x square +c

d. Ln (-8 -2x) +c

7. evaluate the anti derivative of x cos 3x dx

a. 1/6 x square sin 3x +c

b. 1/3 x sin 3x -1/3 sin 3x +c

c. 1/3 x sin 3x+1/9 cos 3x +c

d. 1/2 x square + 1/18 sin square 3x + c

8. evaluate the anti derivative of xe the power of 2x dx

a. 1/6 x square e the power of 3x + c

b. 1/2 xe th power of 2x -1/2e the power of 2x +c

c. 1/2 xe the power of 2x -1/4e the power of 2x + c

d. 1/2 x square - 1/8e the power of 4x + c

9. evaluate the anti derivative of e the power of 3x cosh 2x dx

a. 1/2 e the power of 5x + 1/2 e the power of x + c

b. 1/10 e the power of 5x + 1/2 e the power of x + c

c. 1/4 e the power of 3x + 1/2x + c

d. 1/10 e the power of 5x + 1/5 x +c

10. find the area under one arch of a cycloid described by the parametric equations x=3(2 theta - sin 2 theta) and y=3(1-cos 2 theta). use 0 and pie for the limiting values of theta.

a. 9 pie

b. 18 pie

c. 27 pie

d. 36 pie

11. find the area in the first quadrant bounded by the arc of the circle described by the polar equation r=2 sin theta + 4 cos theta. (on the x-axis theta = 0, and on the y- axis theta =pie/2)

a. 5 pie/2

b. 5 pie/2 + 4

c. 5 pie

d. 5 pie + 8

12. find the length in the first quadrant of the circle described by the polar equation r=2 sin theta + 4 cos theta. the circle is graphed in the accompanying figure.

a. the square root of 2 pie

b. the square root of 5 pie

c. 2 pie

d. 5 pie

13.find the centroid of the area bounded by the parabola y=4-x square and the x-axis.

a. (0, 1.6)

b. (0, 1.7)

c. (0, 1.8)

d. (0, 1.9)

14. find the average value of the function i=15(1-e the power of -1/2t) fro t=0 to t= 4

a. 7.5(1 + e the power or -2)

b. 7.5(2 + e the power of -2)

c. 7.5(2 -e the power of -2)

d. 7.5(3-e the power of -2)

15. find the rms value of the function i=15(1-e the power of -1/z t) from t= 0 to t=4

a. 7.5 the square root of 1+4e the power of -2 -e the power of -4

b. 7.5 the square root of 4-2e the power of -2 + e the power of -4

c. 7.5 the square root of 4+ 4e the power of -2 -e the power of -4

d. 7.5 the square root of 5-2e the power of -2 + e the power of -4

a. 30 degree

b. 45 degree

c. 60 degree

d. 90 degree

15. a line rotates in a horizontal plane according to the equation theta=2t cube - 6t, where theta is the angular position of the rotating line, in radians and t is the time, in seconds. determine the angular acceleration when t=2 sec.

a. 6 radians per sec square

b. 12 radians per sec square

c. 18 radians per sec square

d. 24 radians per sec square

3. evaluate the anti derivative of cot 2x dx.

a. 1/2 Ln sin sx+c

b. 1/2 Ln cos 2x + c

c. 1/2 Ln sec 2x + c

d. 1/2 Ln csc 2x + c

2. evaluate the anti derivative of sin 4x cos square 4x dx.

a. cos cube 4x/3 + c

b. - cos cube 4x/3 + c

c. cos cube 4x/ 12 + c

d. - cos cube 4x/12 + c

3. evaluate the anti derivative of e the power of 3x dx.

a. e the power of 3x + c

b. 1/3 e the power of 3x + c

c. e the power of 4x +c

d. 1/4 e the power of 4x + c

4. which of the following is a step in evaluating the anti derivative of cos square 5x dx

a. the anti derivative of 1+cos 10x/2 dx

b. the anti derivative of 1-cos 10x/2 dx

c. the anti derivative of 1 + cos 10x/20 dx

d. the anti derivative of 1-cos10x/20 dx

5. to evaluate the anti derivative of 3x square cos(2x cube - 4) dx, it is necessary to let

a. u=3x square

b. u=6x

c. u=2x cube - 4

d. u= 6x square

6. evaluate the anti derivative of dx/the square root of 9-8x-x square

a. sin the power of -1(x+4)/5 + c

b. sin the power of -1(x-4)/5 +c

c. Ln the square root of 9-8x-x square +c

d. Ln (-8 -2x) +c

7. evaluate the anti derivative of x cos 3x dx

a. 1/6 x square sin 3x +c

b. 1/3 x sin 3x -1/3 sin 3x +c

c. 1/3 x sin 3x+1/9 cos 3x +c

d. 1/2 x square + 1/18 sin square 3x + c

8. evaluate the anti derivative of xe the power of 2x dx

a. 1/6 x square e the power of 3x + c

b. 1/2 xe th power of 2x -1/2e the power of 2x +c

c. 1/2 xe the power of 2x -1/4e the power of 2x + c

d. 1/2 x square - 1/8e the power of 4x + c

9. evaluate the anti derivative of e the power of 3x cosh 2x dx

a. 1/2 e the power of 5x + 1/2 e the power of x + c

b. 1/10 e the power of 5x + 1/2 e the power of x + c

c. 1/4 e the power of 3x + 1/2x + c

d. 1/10 e the power of 5x + 1/5 x +c

10. find the area under one arch of a cycloid described by the parametric equations x=3(2 theta - sin 2 theta) and y=3(1-cos 2 theta). use 0 and pie for the limiting values of theta.

a. 9 pie

b. 18 pie

c. 27 pie

d. 36 pie

11. find the area in the first quadrant bounded by the arc of the circle described by the polar equation r=2 sin theta + 4 cos theta. (on the x-axis theta = 0, and on the y- axis theta =pie/2)

a. 5 pie/2

b. 5 pie/2 + 4

c. 5 pie

d. 5 pie + 8

12. find the length in the first quadrant of the circle described by the polar equation r=2 sin theta + 4 cos theta. the circle is graphed in the accompanying figure.

a. the square root of 2 pie

b. the square root of 5 pie

c. 2 pie

d. 5 pie

13.find the centroid of the area bounded by the parabola y=4-x square and the x-axis.

a. (0, 1.6)

b. (0, 1.7)

c. (0, 1.8)

d. (0, 1.9)

14. find the average value of the function i=15(1-e the power of -1/2t) fro t=0 to t= 4

a. 7.5(1 + e the power or -2)

b. 7.5(2 + e the power of -2)

c. 7.5(2 -e the power of -2)

d. 7.5(3-e the power of -2)

15. find the rms value of the function i=15(1-e the power of -1/z t) from t= 0 to t=4

a. 7.5 the square root of 1+4e the power of -2 -e the power of -4

b. 7.5 the square root of 4-2e the power of -2 + e the power of -4

c. 7.5 the square root of 4+ 4e the power of -2 -e the power of -4

d. 7.5 the square root of 5-2e the power of -2 + e the power of -4

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