1. Which of the following can be thought of as a special case of the Mean Value Theorem? Intermediate Value Theorem Rolle's Theorem Extreme Value Theorem L'Hopital's rule

2. How many REAL roots does the polynomial x to the fifth +12x-7 have? 0 1 2 3

3. What is the integral from -Pi over 7 to Pi over 7 of Sin(x cubed)? Answer: (Give your answer as a number, using pi if necessary.)

4. What is the integral from 0 to Pi over 2 of (Sine of x divided by the sum of Sine of x and Cosine of x)? Pi over 6 Pi over 2 Pi over 4 Pi over 3

5. Which of the following statements are true? 1. If a function is Continuous on the closed interval between 0 and 1, it must be Riemann integrable. 2. If a function is Riemann Integrable on that interval, it must be continuous there. 3. If a function is bounded on the closed interval containing 0 and 1 its integral must exist there? 1 and 2, but not 3 1 only all 3 1 and 3, but not 2

6. How many roots (real or complex and counting multiple roots the number of times they occur) will a polynomial of degree n have? At least n, but sometimes more We can't tell, we need more information to determine anything At most n, but sometimes less Exactly n

7. Suppose a function satisfies f(0)=1 and f(2)=-1. What can we say about the roots of the function between 0 and 2? There is at least one root, possibly more There is exactly one root Nothing...we need more information There is at most one root, possibly less

8. True or False: If two infinitely differentiable functions match in their value and all their derivatives at a point, then the functions must be the same? True False

9. Are the following statements true or false: A. If a function is differentiable at 0, it is continuous there. B. If a function is differentiable at 0, its derivative is continuous there? B is true, but not A neither are true both are true A is true, but not B

10. You have a double integral of a continuous function over a bounded region, and you calculate it by evaluating the integrals one at a time. Whose theorem did you just use? Answer: (Last name only!)