Horizontal Asymptotes in Terms of Limits
Read this topicExplanations 2
- Just as we can visualize sequence convergence as points on the number line getting closer and closer to some number, we can use a similar visual tool to find what a function ten…
By Max Schindler, Po-Shen Loh, Yang Liu, Moor Xu
- (Video) Horizontal Asymptotes of Limits at Infinity by PatrickJMT Here's a video by patrickJMT showing you how to find the horizontal asymptote of a function whose limit approac…
By Alex Federspiel
Problems 8
- The function f(x)=(2x+5)2x2−4f(x) = \frac{(2x + 5)^2}{x^2 - 4}f(x)=x2−4(2x+5)2 has a horizontal asymptote at y=cy = cy=c. What is ccc?
- Let ppp and qqq be polynomials, and let f(x)=p(x)q(x)f(x) = \frac{p(x)}{q(x)}f(x)=q(x)p(x). If limx→−∞f(x)=c\lim_{x \to -\infty} f(x) = climx→−∞f(x)=c, then what is limx→∞f(…
- Evaluate limx→∞4x3−2x2+6−x3+8\lim_{x\to\infty}{\frac{4x^3-2x^2+6}{-x^3+8}}x→∞lim−x3+84x3−2x2+6
- What values of aaa produce a horizontal asymptote? limx→∞8xa+74x6−27\lim_{x\to\infty}{\frac{8x^a+7}{4x^6-27}}x→∞lim4x6−278xa+7
- Evaluate limx→∞4x−6x3+11+14x4−22x215+6x+2x4−8x3\lim_{x\to\infty}{\frac{4x-6x^3+11+14x^4-22x^2}{15+6x+2x^4-8x^3}}x→∞lim15+6x+2x4−8x34x−6x3+11+14x4−22x2
- What are the only possible horizontal asymptotes? limx→∞axa+xa−1bxb−xb−1\lim_{x\to\infty}{\frac{ax^a+x^{a-1}}{bx^b-x^{b-1}}}x→∞limbxb−xb−1axa+xa−1
- At most how many horizontal asymptotes can a function have?
- Which of the following functions have a horizontal asymptote as x→∞x \rightarrow \inftyx→∞ and have an xxx-intercept at x=1x = 1x=1?