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1. calculate the anti derivative...

1. calculate the anti derivative of x cube dx

a. x square + c

b. 3x square + c

c. x the power of 4 + c

d. x the power of 4/4 + c

2. calculate the anti derivative of x the power of 2/3 dx.

a. 2/3x the power of 2/3 + c

b. 3/2x the power of 2/3 + c

c. 3x the power of 5/3 over 5 + c

d. 5x the power of 5/3 over 3 + c

3. calculate the anti derivative of dx/x square

a. 1/x + c

b. -1/x + c

c. 1/3x cube + c

d. -1/3x cube + c

4. find the area bounded by the curve y= x the power of 1/2 + 2, the x-axis, and the line x=1 and x=4.

a. 7 and 1/2

b. 10 and 2/3

c. 16

d. 28 and 1/2

5. a body is moving along a straight line with a velocity which varies according to the equation v=9t square + 2t, where v is in feet per second and t is in seconds. find the expression for the distance as a function of time.

a. 3t cube + t square + c

b. 3t cube + 2t square + c

c. 18t + c

d. 20t + c

6. if dy/dx= x square + 4, what is the value of y?

a. 2x + c

b. x cube/2 + 4x + c

c. x cube/2 + 2x square + c

d. x cube/3 + 4x + c

7. calculate y as a function of x when dy/dx= 4x cube + 3x square - 6x + 5

a. 4x square + 3x + c

b. 12x square + 6x + c

c. x the power of 4 + x cube - 3x square + 5x + c

d. 4x the power of 4 over 3 + x cube - 6x square + 5x + c

8. when dy/dx=(x-6)the power of 1/2, what does y equal?

a. 1/(x-6)the power of 1/2 +c

b. - __1________________ + c

(x-6)the power of 1/2

c. 2(x-6) the power of 3/2 over 3 + c

d. -2(x-6) the power of 3/2 over 3 + c

9. solve the differential equation: dy/dx=4y square x the power of 1/3

a. 1/y = 3x the power of 4/3 +c

b. 1/y = 3x the power of 4/3 + c/y square

c. -1/y=3x the power of 4/3 + c

d. -2/y cube = 3x the power of 4/3 + c/y square

10. which one of the following is true when ds/dt=3t square/2s

a. s= 3 square root of 6t-3t square + c over 2

b. s= the square root of t cube + c

c. s= the square root of t cube /2 + c

d. s= the square root of 3t/2 + c

11. calculate y when dy/dx= 1/(bx+5)cube

a. -1/2(bx+5)square +c

b. -1/2b(bx + 5) square +c

c. -3/(bx +5) the power of 4 + c

d. -3b/(bx +5) the power of 4 + c

12. find the area lying above the x-axis and below the parabolic curve y=4x-x square

a. 8

b. 8 and 1/3

c. 10 and 2/3

d. 16

number 13,14 and 15 has a graph, if you already have the quastions , i would appriciat it.

16. calculate dy/dx when xy cube + y=3x

a. 3/y cube+1

b. 3/y cube -1

c. 3 + y cube over 1 + 3xy square

d. 3 - y cube over 1+ 3xy square

17. calculate dy/dx when y square = (3x + 1) cube / 9x + 2

a. -3(3x + 1) square/2y(9x + 2) square

b. -3(3x +1) square/y square(9x + 2) square

c. 9(3x +1) square (6x + 1)/2y(9x + 2) square

d. 9(3x + 1) square(6x +1)/ y square(9x + 2) square

18. given the functions y=3x cube + 6x and x=2t square + t, find dy/dt

a. 9t square + 6

b. (9x square + 6)(4t + 1)

c. 9x square + 6/4t + 1

d. 4t + 1/9x square + 6

19. find dy/dx when y=cosh(bx square)

a. 2bx cosh (bx square)

b. -2bx cosh (bx square)

c. 2bx sinh (bx square)

d. -2bx sinh (bx square)

20. find dy/dx when y=Ln(sinh 2x)

a. 2 cosh 2x

b. 2 coth 2x

c. 2 sech 2x

d. 2 csch 2x

21. find dy/dx when sinh 3y=cos 2x

a. -2 sin 2x

b. -2 sin sx/sinh3y

c. -2/3 tan(2x/3y)

d. -2 sin 2x/3 cosh 3y

22. find the derivative of y=cos(x square) with respect to x.

a. - sin(2x)

b. -2x sin (x square)

c. - sin (2x) cos ( x square)

d. -2x sin (x square) cos (x square)

23. find the derivative of y=sin square (4x) cos (3x) with respect to x.

a. 8 sin (4x) cos (3x) -3 sin square(4x) sin (3x)

b. 8 cos(4x) cos (3x) -3 sin square(4x) sin ( 3x)

c. 8 sin (4x) cos (4x) cos (3x) -3 sin square (4x) sin (3x)

d. 8 sin (4x) cos (4x) cos (3x)-3 sin square (4x) sin (3x) cos(3x)

24. find the derivative of y=e the power of bx square with respect to x.

a. be the power of bx square

b. bxe the power of bx square

c. 2 bxe the power of bx square

d. bx square e the power of bx square

25. calculate dy/dx when y=(x square + 2)e the power of 4x as the derivative of a product, letting u=x square + 2 and v=e the power of 4x. which of the following is a step in your solution?

a. du/dx=2x+2

b. du/dx=2x

c. dv/dx = 4xe the power of 3x

d. dv/dx = 4xe the power of 4x

26. which of the following represents dy/dx when y=e the power of -2x sec(3x)?

a. 3e the power of -2x sec (3x) tan (3x) -2e the power of -2x sec(3x)

b. 3e the power of -2x sec (3x) tan (3x) -2xe the power of -2x sec (3x)

c. 3e the power of -2x sec(3x) tan (x)-2e the power of -2x sec (3x)

d. 3e the power of -2x sec (3x) tan (x) -2xe the power of -2x sec(3x)

27. calculate dy/dx if y= Ln(2x cube + 3x)

a. 1/2x cube + 3x

b. 1/ 6x square + 3

c. 2x cube + 3x/6x square + 3

d. 6x square + 3/ 2x cube + 3x

28. calculate dy/dx if Ln(x+y)=x/e the power of y

29. given the curve that is described by the equation r=3 cos theta, find the angle that the tangent line makes wit

a. x square + c

b. 3x square + c

c. x the power of 4 + c

d. x the power of 4/4 + c

2. calculate the anti derivative of x the power of 2/3 dx.

a. 2/3x the power of 2/3 + c

b. 3/2x the power of 2/3 + c

c. 3x the power of 5/3 over 5 + c

d. 5x the power of 5/3 over 3 + c

3. calculate the anti derivative of dx/x square

a. 1/x + c

b. -1/x + c

c. 1/3x cube + c

d. -1/3x cube + c

4. find the area bounded by the curve y= x the power of 1/2 + 2, the x-axis, and the line x=1 and x=4.

a. 7 and 1/2

b. 10 and 2/3

c. 16

d. 28 and 1/2

5. a body is moving along a straight line with a velocity which varies according to the equation v=9t square + 2t, where v is in feet per second and t is in seconds. find the expression for the distance as a function of time.

a. 3t cube + t square + c

b. 3t cube + 2t square + c

c. 18t + c

d. 20t + c

6. if dy/dx= x square + 4, what is the value of y?

a. 2x + c

b. x cube/2 + 4x + c

c. x cube/2 + 2x square + c

d. x cube/3 + 4x + c

7. calculate y as a function of x when dy/dx= 4x cube + 3x square - 6x + 5

a. 4x square + 3x + c

b. 12x square + 6x + c

c. x the power of 4 + x cube - 3x square + 5x + c

d. 4x the power of 4 over 3 + x cube - 6x square + 5x + c

8. when dy/dx=(x-6)the power of 1/2, what does y equal?

a. 1/(x-6)the power of 1/2 +c

b. - __1________________ + c

(x-6)the power of 1/2

c. 2(x-6) the power of 3/2 over 3 + c

d. -2(x-6) the power of 3/2 over 3 + c

9. solve the differential equation: dy/dx=4y square x the power of 1/3

a. 1/y = 3x the power of 4/3 +c

b. 1/y = 3x the power of 4/3 + c/y square

c. -1/y=3x the power of 4/3 + c

d. -2/y cube = 3x the power of 4/3 + c/y square

10. which one of the following is true when ds/dt=3t square/2s

a. s= 3 square root of 6t-3t square + c over 2

b. s= the square root of t cube + c

c. s= the square root of t cube /2 + c

d. s= the square root of 3t/2 + c

11. calculate y when dy/dx= 1/(bx+5)cube

a. -1/2(bx+5)square +c

b. -1/2b(bx + 5) square +c

c. -3/(bx +5) the power of 4 + c

d. -3b/(bx +5) the power of 4 + c

12. find the area lying above the x-axis and below the parabolic curve y=4x-x square

a. 8

b. 8 and 1/3

c. 10 and 2/3

d. 16

number 13,14 and 15 has a graph, if you already have the quastions , i would appriciat it.

16. calculate dy/dx when xy cube + y=3x

a. 3/y cube+1

b. 3/y cube -1

c. 3 + y cube over 1 + 3xy square

d. 3 - y cube over 1+ 3xy square

17. calculate dy/dx when y square = (3x + 1) cube / 9x + 2

a. -3(3x + 1) square/2y(9x + 2) square

b. -3(3x +1) square/y square(9x + 2) square

c. 9(3x +1) square (6x + 1)/2y(9x + 2) square

d. 9(3x + 1) square(6x +1)/ y square(9x + 2) square

18. given the functions y=3x cube + 6x and x=2t square + t, find dy/dt

a. 9t square + 6

b. (9x square + 6)(4t + 1)

c. 9x square + 6/4t + 1

d. 4t + 1/9x square + 6

19. find dy/dx when y=cosh(bx square)

a. 2bx cosh (bx square)

b. -2bx cosh (bx square)

c. 2bx sinh (bx square)

d. -2bx sinh (bx square)

20. find dy/dx when y=Ln(sinh 2x)

a. 2 cosh 2x

b. 2 coth 2x

c. 2 sech 2x

d. 2 csch 2x

21. find dy/dx when sinh 3y=cos 2x

a. -2 sin 2x

b. -2 sin sx/sinh3y

c. -2/3 tan(2x/3y)

d. -2 sin 2x/3 cosh 3y

22. find the derivative of y=cos(x square) with respect to x.

a. - sin(2x)

b. -2x sin (x square)

c. - sin (2x) cos ( x square)

d. -2x sin (x square) cos (x square)

23. find the derivative of y=sin square (4x) cos (3x) with respect to x.

a. 8 sin (4x) cos (3x) -3 sin square(4x) sin (3x)

b. 8 cos(4x) cos (3x) -3 sin square(4x) sin ( 3x)

c. 8 sin (4x) cos (4x) cos (3x) -3 sin square (4x) sin (3x)

d. 8 sin (4x) cos (4x) cos (3x)-3 sin square (4x) sin (3x) cos(3x)

24. find the derivative of y=e the power of bx square with respect to x.

a. be the power of bx square

b. bxe the power of bx square

c. 2 bxe the power of bx square

d. bx square e the power of bx square

25. calculate dy/dx when y=(x square + 2)e the power of 4x as the derivative of a product, letting u=x square + 2 and v=e the power of 4x. which of the following is a step in your solution?

a. du/dx=2x+2

b. du/dx=2x

c. dv/dx = 4xe the power of 3x

d. dv/dx = 4xe the power of 4x

26. which of the following represents dy/dx when y=e the power of -2x sec(3x)?

a. 3e the power of -2x sec (3x) tan (3x) -2e the power of -2x sec(3x)

b. 3e the power of -2x sec (3x) tan (3x) -2xe the power of -2x sec (3x)

c. 3e the power of -2x sec(3x) tan (x)-2e the power of -2x sec (3x)

d. 3e the power of -2x sec (3x) tan (x) -2xe the power of -2x sec(3x)

27. calculate dy/dx if y= Ln(2x cube + 3x)

a. 1/2x cube + 3x

b. 1/ 6x square + 3

c. 2x cube + 3x/6x square + 3

d. 6x square + 3/ 2x cube + 3x

28. calculate dy/dx if Ln(x+y)=x/e the power of y

29. given the curve that is described by the equation r=3 cos theta, find the angle that the tangent line makes wit

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