1. Which of the following is a simplification for :

log(3x)+log(x)

 
 
 
 

2. Which of the following is a simplification for :

log(7x)+log(3xy)-log(3x)

 
 
 
 

3.

 
 
 
 

4.

 
 
 
 

5.

 
 
 
 

6. Evaluate the derivative of the following function using the limit definition:

f(x)=x2

 
 
 
 

7. Evaluate the derivative of the following function using the limit definition:

f(x)=cos(x)

 
 
 
 

8. Identify the derivative of the following:

f(x)=9x4+3x

 
 
 
 

9. Identify dy/dx for the following using implicit differentiation:

2y2+2x2=4

 
 
 
 

10. Identify dy/dx for the following :

2y = 3x3 + cos(x)

 
 
 
 

11. Evaluate:

∫(4x7+5x3+7x+5)dx

 
 
 
 

12. Evaluate:

∫ln(x)/xdx

 
 
 
 

13. Use a right Riemann sum with 4 sub-intervals to estimate:

∫40(x<sup>4</sup>+5)dx

 
 
 
 

14.

 
 
 
 

15. Use a Midpoint Riemann sum with 2 sub-intervals to estimate:

∫40(x2+1)dx

 
 
 
 

16. Use the following table to calculate a right Riemann sum on the interval [0,4], (Δx =1)

x 0 1 2 3 4
f(x) 5 7 1 6 8
 
 
 
 

17. ∫sin3(x)dx

 
 
 
 

18. ∫sin2(x)cos2(x)dx

 
 
 
 

19. ∫sec4(x)tan4(x)dx

 
 
 
 

20. Eliminate the parameter for the following. What do these  parametric equations represent in the x – y plane?

x = sin(t)        y = cos(t)

 
 
 
 

Question 1 of 20