Evaluating Limits: Examples Use the investigative method to evaluate the following limit: 1. lim x X-2 Use the direct substitution to evaluate the following limits: 1. lim x x-2 2. lim x-1 x-3x+2 3. lim x +9 X-14 Example: Use the graph of the following function y = f(x) to estimate the x-0 following limits: a. lim f(x) x-1- b. lim f(x) e. lim f(x) x-2* g. lim f(x) X-4 h. lim f(x) x-4 d. lim_f(x) x-2 c. lim f(x) X-O f. lim f(x) x-2 i. lim f(x) x-4 5 4 3 f 2 1- -1 1 2 3 4 5 -1- -2- Example: 3. Let f(x) = -x, x 2. N 2 4 f(x) and lim,-- f(x). f(x) exist? If so, what is it? If not, why not? f(x) and lim,-4* f(x). f(x) exist? If so, what is it? If not, why not? a. Find lim, b. Does lim, c. Find lim, d. Does lim, 3-x, x 2. 4. Let f(x) = 2. y=3-x m 0 2 KIN a. Find lim, f(x), lim, f(x), and f(2). b. Does limx-2 f(x) exist? If so, what is it? If not, why not? c. Find lim, d. Does lim, -1- f(x) and lim, f(x). f(x) exist? If so, what is it? If not, why not?