NAME____________________________________________

Student ID _________________________________________

Signature __________________________________________

Exam Grade ________

Semester Grade ______

Final Grade _________

Show all of your work and circle your answers

Each problem is worth 5 points

YOU MUST SHOW WORK OR DESCRIBE CALCULATOR FUNCTIONS USED FOR ALL PROBLEMS TO RECEIVE FULL CREDIT

1. Find the vertical and horizontal asymptotes for the function

Vertical Asymptote:__________________________

Horizontal Asymptote:________________________

2. Use the definition of derivative to find the slope of the tangent line to f(x) = (x - 1)(x + 1)

3. Find dy/dx for the following:

dy/dx:___________________________

dy/dx:____________________________

dy/dx:____________________________

4. Find B so the function is continuous:

B=:_______________________

Is the function differentiable at the point -1? Explain?

5. One car drives east at 40 mph. while a second car drives south at 30 mph. How much is the distance between them changing one hour later?

Answer:_______________________

6. Limits:

Answer:_______________________

Answer:_______________________

Answer:_______________________

7. Find all critical ponts for f(x) = (ln x)³ - 5 ln x + 6

Answer:_______________________

How would you determine if the critical point was a max or a min without graphing?

Answer:_______________________

8. Find dy/dx for x³ = 27 - y² + tan (y)

Answer:_______________________

Find the equation of the line tangent to the graph at (3,0)

Answer:_______________________

9. After collecting sales data over twenty years, a curve b(x) is found to accurately describe the amount of books people will buy as a function of the price x. What is price should be asked to realize the maximum revenue when b(x) = e ^-.01x ?

Answer:_______________________

10. A cylindrical can is to be made of 10 square inches of steel. What is the maximum volume?

Answer:_______________________

11. Given a function y = x³ - 5x² + 3x + 2

Determine when the function is both decreasing and concave up.

Answer:_______________________

12. Given the graph of the derivative, For what values of x is the function a max? Min? Inflection point?

Max:_______________________

Min:_______________________

Inflection:__________________

13. Without a calculator, use calculus to show how you could approximate the fourth root of 19?

Answer:_______________________

14. If P''(x) = x - 2 , and P'(0) = 5 and P (1) = -3, find P(x).

Answer:_______________________

15. Find the upper and lower limits to the area under the unit circle and between the x and y axis using Reiman sums. Assume there are 4 equally spaced partitions.

Upper Bound:_______________________

Lower Bound:_______________________

16. Sketch the area under the curve given by y = (x + 5) (3 - x) and above the x-axis.

Find the area exactly by using calculus

Answer:_______________________

17. Evaluate:

Answer:_______________________

Answer:_______________________

18 Evaluate:

Answer:_______________________

Answer:_______________________

Answer:_______________________

19.

Answer:_______________________

Answer:_______________________

Answer:_______________________

20. What is calculus?

What exactly is being studied in calculus?

What relevance are the objects studied in calculus to you?