MATH 221 In-Class Exercises on Limits

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1. Compute each of the following limits and show your work.

2. Find all values of a such that exists. What is the value of the limit in those cases?

3. Let . a) What is the domain of f(x)?

b) At what values of c does exist?

c) At what values of c does fail to exist?

d) Graph the function f(x).

e) What is the range of f(x)?

f) For each of the values of c at which does not exist find .

4. a) Graph the function .

b) Estimate using the calculator.

c) Suppose x is a very small positive number. Express and without the absolute value signs. (Hint: for a small positive x is 2x-1 positive or negative.)

d) Suppose that x is a negative number very close to 0. . Express and without the absolute value signs.

e) Use what you found in parts c) and d) to compute .

5. Find numbers a and b such that .

6. a) Find the domain of and graph the function.

b) For what values of c does exist?

c) Find the one value for which one of the one sided limits of f(x) exists but the other does not.