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Practice Problems
\(\textbf{1)}\) \(\displaystyle\lim_{x\to \infty}\frac{5x^2-10}{6x^2+1}\)
\(\textbf{2)}\) \(\displaystyle\lim_{x\to \infty}\frac{x^2+5x+1}{x^2+5x+100}\)
\(\textbf{3)}\) \(\displaystyle\lim_{x\to \infty}\frac{5x^2+2x-10}{3x^2+4x-5}\)
\(\textbf{4)}\) \(\displaystyle\lim_{x\to \infty}\frac{8x-10}{4x-5}\)
\(\textbf{5)}\) \(\displaystyle\lim_{x\to \infty}\frac{3\sqrt{x}-4x^{1.5}}{x-2+\sqrt{x}}\)
\(\textbf{6)}\) \(\displaystyle\lim_{x\to \infty}\frac{8\sqrt{x}+x^2}{4x-x^2}\)
\(\textbf{7)}\) \(\displaystyle\lim_{x\to\, -\infty}\frac{\sqrt{16x^4-3x}}{2x^2+3}\)
\(\textbf{8)}\) \(\displaystyle\lim_{x\to\, -\infty}x^4+x^3\)
\(\textbf{9)}\) \(\displaystyle\lim_{x\to \infty}\frac{4-6e^x}{2+2e^x}\)
\(\textbf{10)}\) \(\displaystyle\lim_{x\to \infty}e^{-x} \cos x\)
\(\textbf{11)}\) \(\displaystyle\lim_{x\to \infty}-2 \sin x\)
\(\textbf{12)}\) \(\displaystyle\lim_{x\to \infty}\frac{5x+4}{x^2-3}\)
\(\textbf{13)}\) \(\displaystyle\lim_{x\to -\infty}\frac{2x-3}{7x-3}\)
\(\textbf{14)}\) \(\displaystyle\lim_{x\to \infty}\frac{5x^2+4}{x^3+4x^2-3}\)
\(\textbf{15)}\) \(\displaystyle\lim_{x\to \infty}e^{-2x} \sin x\)
\(\textbf{16)}\) \(\displaystyle\lim_{x\to \infty}e^{-2x} + \sin x\)
\(\textbf{17)}\) \(\displaystyle\lim_{x\to \infty}\left(\sqrt{4x^2+3x}-2x \right)\)
\(\textbf{18)}\) \(\displaystyle\lim_{x\to -\infty}\left(\sqrt{4x^2+6x}+2x \right)\)
See Related Pages\(\)
\(\bullet\text{ Limit Calculator}\)
\(\,\,\,\,\,\,\,\,\text{(Symbolab.com)}\)
\(\bullet\text{ Calculus Homepage}\)
\(\,\,\,\,\,\,\,\,\text{All the Best Topics…}\)
\(\bullet\text{ Limits on Graphs}\)
\(\,\,\,\,\,\,\,\,\)
\(…\)
\(\bullet\text{ Continuity on Graphs}\)
\(\,\,\,\,\,\,\,\,\)\(…\)
\(\bullet\text{ Piecewise Functions- Limits and Continuity}\)
\(\,\,\,\,\,\,\,\,\)
\(…\)
\(\bullet\text{ Infinite Limits}\)
\(\,\,\,\,\,\,\,\,\displaystyle \lim_{x\to 4^{+}} \frac{5}{x-4}…\)
\(\bullet\text{ Trig Limits}\)
\(\,\,\,\,\,\,\,\,\displaystyle \lim_{\theta\to0} \frac{\sin \theta}{\theta}=1…\)
In Summary
Limits at infinity evaluate the function value when x approaches infinity or negative infinity. In some cases functions increase or decrease without bound. And in other cases the functions will approach a finite value. When it approaches a finite value, we are ultimately finding the horizontal asymptote.
Limits at infinity are typically covered in Calculus I.
About Andymath.com
Andymath.com is a free math website with the mission of helping students, teachers and tutors find helpful notes, useful sample problems with answers including step by step solutions, and other related materials to supplement classroom learning. If you have any requests for additional content, please contact Andy at tutoring@andymath.com. He will promptly add the content.
Topics cover Elementary Math, Middle School, Algebra, Geometry, Algebra 2/Pre-calculus/Trig, Calculus and Probability/Statistics. In the future, I hope to add Physics and Linear Algebra content.
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