Math Sample Test

Section 1
no calculator allowed

1. Compute the fol lowing limits algebraically . Show your work. Please distinguish between infinite limits
and limits that do not exist.

2. Write the equation of the line with slope -1/2 at the point . Show your work.

3. Ex press the given quantity as a single logarithm (with no constant term in front )

ln(a + b) + 2 ln(a) - ln(a - b).

4. Graph the function y =π - cos^-1(x - 2). Be sure to include the range and domain of the function.

Section 2
calculator allowed

5. Find c so that the function f(x) is continuous, where

Show your work.

6. True or False. Mark each statement as true (T) or false (F). Partial credit may be given for good
explanations even if the answer is incorrect.

If exists and exists, then must exist.

If , then .
If f and g are functions, then .
If a function is continuous on its domain, then the limit of the function is defined at all real numbers .

7. Consider the functions and . For what values of x if any is g(x) ≥ f(x).

8. Let f(x) and g(x) be functions drawn in class on Friday. Find the following limits if they exist.

9. Explain the meaning of the intermediate value theorem using a graph. Suppose f(x) = x³ + 2x - 9,
use the intermediate value theorem to show that f(x) has a root . (10 points)