2. LIMITS INVOLVING INFINITY Mrs. Erickson

3. Limits Involving Infinity Definition: y = b is a horizontal asymptote if either lim f(x) = b or lim f(x) = b x  ∞x  -∞ Find: lim = sin(x) x x  ∞ Definition: x = a is a vertical asymptote if either lim f(x) = ±∞ or lim f(x) = ±∞ x  a-x  a- x  a+x  a+

4. Limits Involving Infinity End Behavior Models: f(x) = 3x 4 + … g(x) = 3x 4 For very large values of x, these two functions are quite similar. f(x) = Same as f(x) = x 2 g(x) = Same as g(x) = h(x) = Same as h(x) = 2x 5 + … 3x 3 + … 2x 3 + … 3x 3 + … 4x 2 + … 2x 3 + … 2323 2323 2x2x

5. The End