Lesson 3.5 Limits at Infinity. From the graph or table, we could conclude that f(x) → 2 as x → Graph What is the end behavior of f(x)? Limit notation:

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Presentation transcript:

Lesson 3.5 Limits at Infinity

From the graph or table, we could conclude that f(x) → 2 as x → Graph What is the end behavior of f(x)? Limit notation: and

Definition of Limits At Infinity (translation): means that the distance between the function and the limit will decrease for larger (smaller) and larger (smaller) x values

Finding Limits at Infinity Same as finding the horizontal asymptote Can be found by dividing each term by highest degree of variable Rational Function Rules: If n < d → → If n = d → → If n > d →→ no horizontal asymptote or infinite limit ratio of leading coefficients

x→∞

Example 1

Example 2

x→∞

Infinite Limits & One Sided Limits For functions that increase (decrease) without bound, the limit approaches ∞ (- ∞ ) Problem Set 3.5