## 2.6 Limits at Infinity Horizontal Asymptotes 1. Overview 2. Examples

In the second case the graph flattens out on the left

limits at infinity

## Chapter 5 Section 5

“y approaches negative infinity as x approaches 0 from the left” The line y = b is a horizontal asymptote of the function y = f (x) if.

math rational functions

## Limits as x approaches Infinity

Horizontal Asymptotes. Geometrically lim x→+∞ f(x) = L means that the graph of f(x) approaches the horizontal line y = L at infinity

RGASC CMath Limits as x approaches Infinity

## 301 Final

Horizontal Asymptote: As x approaches infinity or negative infinity Finding Oblique Asymptotes: In the rational function

CST

## 2.5 Limits at Infinity

Therefore the graph of y = 2 + 10>x2 approaches the horizontal asymptote y = 2 as x S ∞ and as x S - ∞ (Figure 2.32). b. The numerator of sin x> 1x is

SE C S

## Untitled

What about analytically finding horizontal asymptotes? When x approaches infinity or negative infinity the numerator and denominator will take the form.

. limits involving infinity p.

## Graphing the curve y =

since the denominator approaches infinity while the numerator is constant. Thus there is no horizontal asymptote approached as x approaches −∞.

graphingExample

## Prompt Students are studying multiplying binomials (factoring and

If n < m then the x-axis is the horizontal asymptote. When a>b

Situation Rational Functions

## Types of Graphs Inverse Functions Logarithms and Exponentials

Horizontal Asymptote. A Horizontal Asymptote is the y-value that a graph approaches as x approaches positive or negative infinity.

APCalcABResources RidgefieldHS

## Slant Asymptotes If limx→∞[f(x) − (ax + b)] = 0 or lim x

f(x) approaches the graph of the line y = ax + b as x approaches ∞. [ Note: If a = 0 this is a horizontal asymptote]. In the case of rational functions

. Summary of Curve Sketching

- horizontal asymptote limit as x approaches infinity
- horizontal asymptote as x approaches negative infinity