Horizontal asymptotes Determine limx →∞ f(x) and limx →-∞ f(x) for the following functions. Then

step 1 We need to find the limit of the given function f x is equal to 2x plus 1 divided by 3 x rist po

Horizontal asymptotes Determine limx →∞ f(x) and limx →-∞...

Horizontal asymptotes Determine $\lim _{x \rightarrow \infty} f(x)$ and $\lim _{x \rightarrow-\infty} f(x)$ for the following functions. Then give the horizontal asymptotes of $f(\text {if any})$.
$$f(x)=\frac{2 x+1}{3 x^{4}-2}$$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Degree Comparison in Polynomials

For rational functions expressed as a ratio of polynomials, comparing the highest power (degree) in the numerator and denominator is crucial. This comparison reveals which component of the function dominates as x grows large or becomes very negative, thereby guiding the determination of the function's end behavior and any horizontal asymptote.

Horizontal Asymptotes

A horizontal asymptote is a horizontal line y = L that a function approaches as x tends toward infinity or negative infinity. It describes the end behavior of a function and can be determined by calculating the limits of the function as x ? +? and x ? -?.

Limits of Rational Functions at Infinity

Evaluating the limits of rational functions as x approaches infinity or negative infinity involves examining the degrees of the numerator and denominator. When the degree of the numerator is less than the denominator, as x becomes very large in magnitude, the function typically approaches zero, leading to a horizontal asymptote at y = 0.

Transcript

Please give Ace some feedback