1.) Use calculus to find the exact absolute maximum and absolute minimum values of on the interval . ( 8 points )

2. ) If and for , how small can possibly be ?

( 6 points )

3. ) Use Newton’s Method to find all roots of the equation correct to six decimal places. ( 8 points )

Find the following limits : ( 7 points each )

4. )

5. )

6. ) Sketch the graph of a function that satisfies all of the given conditions : , , , , if ,

on and , on and ,

on and , on . ( 7 points )

7. ) Given the equation use the guidelines of Chapter 4 to find the

following :

a. ) Domain : ( 4 points )

b. ) Exact Intercepts : ( 6 points )

c. ) Symmetry : ( 4 points )

d. ) Exact Asymptotes : ( 6 points )

e. ) Exact Intervals of Increasing and Decreasing : ( 6 points )

f. ) Exact Local Maximum and Minimum Values : ( 5 points )

g. ) Concavity : ( 5 points )

h. ) Exact Points of Inflection : ( 5 points )

i. ) Sketch the Curve : ( 6 points )