Example 1. Evaluate the following limits: 9x3 - 6x2 - 2x (a) lim x-+00 6 - 10x - 923 (b) lim 35x - 7x+9 7->-0 15x + 323/2 - 12 (2x - 3) (1 -22) (c) lim x-7-00 (202 + 1) (5 - 20)Reflection 2. What is a general rule for determining the horizontal/slant asymptotes of rational functions and how is that related to finding the limits at infinity? Example 3. Find the horizontal / slant asymptotes of the following functions (a) f (2) = - 2(2 + 2) x2 + 6x + 9 2-3 (b) g(x) = 22 - 16Problem 4. Write a function that has a horizontal asymptote at y = 2 and vertical asymptotes at x = -1 and x = 5 Problem 5. Write a function that has a slant asymptote y = 2x and vertical asymptotes at x = -1 and x = 5