In symbol, we write this as

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2.2 Limits Involving Infinity

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Presentation transcript:

In symbol, we write this as LIMIT AT INFINITY Consider the function Investigate the behavior of f(x) as x decreases without bound x -1 -5 -10 -100 -1000 -10,000 f(x) 1 1.92 1.98 1.9998 1.999998 1.99999998 In symbol, we write this as

In symbol, we write this as Consider the function Investigate the behavior of f(x) as x increases without bound x 1 5 10 100 1000 10,000 f(x) 1.92 1.98 1.9998 1.999998 1.99999998 In symbol, we write this as

horizontal asymptote

Theorem : Let n be a positive integer, then

Horizontal asymptote

x = -2 (vertical asymptote) y = 2 is a horizontal asymptote Dh: all x R except x = -2 When x = 0 , y = - 3 (y – int) When y = 0 , x = 3 (x – int) x = -2 (vertical asymptote) y = 2 is a horizontal asymptote x - 4 - 3 - 1 y = h(x) 7 12 - 8 9

x = -2 (vertical asymptote) y = 2 is a horizontal asymptote Dh: all x R except x = -2 horizontal asymptote y = 2 x = -2 (vertical asymptote) x - 4 - 3 - 1 y = h(x) 7 12 - 8 (0, -3) , (3, 0) vertical asymptote x = -2 y = 2 is a horizontal asymptote 10

Df: all x R except x = -2 & x = 2 When x = 0 , (y – int) When y = 0 , x = -1 (x – int) x = -2 (vertical asymptote) x = 2 (vertical asymptote) x -4 -3 -1.5 1 3 4 f(x) (-1/4) (-2/5) (2/7) (-2/3) (4/5) (5/12) -0.25 -0.4 0.286 -0.67 0.8 0.417 y = 0 (horizontal asymptote) 11

Df: all x R except x = -2 & x = 2 x = -2 (vertical asymptote) vertical asymptote horizontal asymptote x = -2 y = 0 x = 2 (vertical asymptote) x = 2 vertical asymptote y = 0 (horizontal asymptote) x -4 -3 -1.5 1 3 4 f(x) (-1/4) (-2/5) (2/7) (-2/3) (4/5) (5/12) -0.25 -0.4 0.286 -0.67 0.8 0.417 12