NOTES 1.3 Limits at Infinity.pdf - Notes 1.3 Limits at Infinity §1.3—Limits at Infinity When we take the limit of a function at infinity we are

# NOTES 1.3 Limits at Infinity.pdf - Notes 1.3 Limits at...

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Notes 1.3: Limits at Infinity Page 1 of 4 §1.3—Limits at Infinity When we take the limit of a function at infinity, we are interested in the end-behavior of a graph. We can write the analysis of each end-behavior of a function f x ( using the following notations: lim ( ) x f x →∞ or lim ( ) x f x →-∞ Assuming a function exists on either end, for infinitely large and infinitely small values of x , it is limited in what it can do. We will now analyze these possibilities. Example 1: Evaluate the following limits without a calculator: (a) lim x →∞ 3 x 5 - 4 x 3 + 2 x 2 - 7 x + 11 ( = (b) lim x →-∞ 3 x 5 - 4 x 3 + 2 x 2 - 7 x + 11 ( = (c) lim x →∞ e - x = (d) lim x →-∞ e - x = (e) lim x →∞ sin x = (f) lim x →-∞ x sin x = (g) lim x →∞ 1 x sin x = The last case is of particular interest to all math teachers, most math students, and very few chimpanzees. Here’s why: Definition: lim ( ) x f x L →∞ = or lim ( ) x f x L →-∞ = f x ( has a Horizontal Asymptote (HA) at y L = Horizontal Asymptotes are NOT, repeat, NOT discontinuities.

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