1. Miss Battaglia AP Calculus AB/BC

2. x -∞  -100-100110100 ∞∞ f(x) 33 2.99972.971.50 2.972.9997 33 f(x) approaches 3 x decreases without bound x increases without bound f(x) approaches 3

3. Let L be a real number. 1. The statement means that for each ε>0 there exists an M>0 such that |f(x)-L| M. 2. The statement means that for each ε>0 there exists an N<0 such that |f(x)-L|<ε whenever x<N.

4. The line y=L is a horizontal asymptote of the graph of f if or

5. If r is a positive rational number and c is any real number, then Furthermore, if x r is defined when x<0, then

6. Find the limit:

8. Find each limit. a. b. c.

9. 1. If the degree of the numerator is less than the degree of the denominator, then the limit of the rational function is 0. 2. If the degree of the numerator is equal to the degree of the denominator, then the limit of the rational function is the ratio of the leading coefficients. 3. If the degree of the numerator is greater than the degree of the denominator, then the limit of the rational function does not exist.