If you just need practice with limits problems for now, previous students have found what’s below super-helpful. And if you have questions, please ask on our Forum!

Are you working to solve problems about $\displaystyle{\lim_{x \to \infty}}$ and $\displaystyle{\lim_{x \to\, -\infty}}$? Let’s look at common limit at infinity problems and solutions so you can learn to solve them routinely.

CALCULUS SUMMARY: Limits at Infinity

Here’s a summary of our in-depth treatment of Limits at Infinity. You can access that material, including specifically-designed Desmos graphing calculators that illustrate the main points, for free in the Section of our site specifically about Limits at Infinity.

To access more problems and solutions, including AP-style multiple choice questions, log in for free with your Google, Apple or Facebook account, or create a dedicated Matheno in 60 seconds. You’ll also then be able to mark the problems *you* want to be sure to review before your exams. Simply use the log-in area at the bottom of this screen.

Problem #1: Polynomial

Problem #2: Numerator & denominator have the same highest power

Find $\displaystyle{\lim_{x \to \infty}\frac{5x^2 -7}{3x^2 + 8}}.$

Problem #3: Denominator has highest power

Find $\displaystyle{\lim_{x \to \infty}\frac{4x^3 + 2x -24}{x^4 – x^2 + 84 } }.$

Problem #4: Numerator has the highest power

Find $\displaystyle{\lim_{x \to \infty}\frac{x^3 +2}{3x^2 + 4}}.$

Problem #5: sin & cos

Limit at Infinity Problems with Square Roots

Want access to *all* of our Calculus problems and solutions? Sign in for free with your Google, Facebook or Apple account, or with your dedicated Matheno account (which you can create in 60 seconds). Then visit our Calculus Home screen.

And if you have a question about a limit-at–infinity problem you could use some help with, or about limits in general, please pop over to our Forum and post. We’ll be happy to assist!

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