Practice Problems
\(\textbf{1)}\) \(\displaystyle\lim_{x\to \infty}\frac{5x^2-10}{6x^2+1}\)
\(\textbf{2)}\) \(\displaystyle\lim_{x\to \infty}\frac{x^2+5x+1}{x^2+5x+100}\)
\(\textbf{3)}\) \(\displaystyle\lim_{x\to \infty}\frac{5x^2+2x-10}{3x^2+4x-5}\)
\(\textbf{4)}\) \(\displaystyle\lim_{x\to \infty}\frac{8x-10}{4x-5}\)
\(\textbf{5)}\) \(\displaystyle\lim_{x\to \infty}\frac{3\sqrt{x}-4x^{1.5}}{x-2+\sqrt{x}}\)
\(\textbf{6)}\) \(\displaystyle\lim_{x\to \infty}\frac{8\sqrt{x}+x^2}{4x-x^2}\)
\(\textbf{7)}\) \(\displaystyle\lim_{x\to\, -\infty}\frac{\sqrt{16x^4-3x}}{2x^2+3}\)
\(\textbf{8)}\) \(\displaystyle\lim_{x\to\, -\infty}x^4+x^3\)
\(\textbf{9)}\) \(\displaystyle\lim_{x\to \infty}\frac{4-6e^x}{2+2e^x}\)
\(\textbf{10)}\) \(\displaystyle\lim_{x\to \infty}e^{-x} \cos x\)
\(\textbf{11)}\) \(\displaystyle\lim_{x\to \infty}-2 \sin x\)
\(\textbf{12)}\) \(\displaystyle\lim_{x\to \infty}\frac{5x+4}{x^2-3}\)
\(\textbf{13)}\) \(\displaystyle\lim_{x\to -\infty}\frac{2x-3}{7x-3}\)
\(\textbf{14)}\) \(\displaystyle\lim_{x\to \infty}\frac{5x^2+4}{x^3+4x^2-3}\)
\(\textbf{15)}\) \(\displaystyle\lim_{x\to \infty}e^{-2x} \sin x\)
\(\textbf{16)}\) \(\displaystyle\lim_{x\to \infty}e^{-2x} + \sin x\)
\(\textbf{17)}\) \(\displaystyle\lim_{x\to \infty}\left(\sqrt{4x^2+3x}-2x \right)\)
\(\textbf{18)}\) \(\displaystyle\lim_{x\to -\infty}\left(\sqrt{4x^2+6x}+2x \right)\)
\(\textbf{19)}\) \(\displaystyle\lim _{x\to \infty \:}\left(\frac{\sin \left(x\right)}{x}\right)\)
See Related Pages\(\)
\(\bullet\text{ Limit Calculator}\)
\(\,\,\,\,\,\,\,\,\text{(Symbolab.com)}\)
\(\bullet\text{ Calculus Homepage}\)
\(\,\,\,\,\,\,\,\,\text{All the Best Topics…}\)
\(\bullet\text{ Limits on Graphs}\)
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\(…\)
\(\bullet\text{ Continuity on Graphs}\)
\(\,\,\,\,\,\,\,\,\)\(…\)
\(\bullet\text{ Piecewise Functions- Limits and Continuity}\)
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\(…\)
\(\bullet\text{ Infinite Limits}\)
\(\,\,\,\,\,\,\,\,\displaystyle \lim_{x\to 4^{+}} \frac{5}{x-4}…\)
\(\bullet\text{ Trig Limits}\)
\(\,\,\,\,\,\,\,\,\displaystyle \lim_{\theta\to0} \frac{\sin \theta}{\theta}=1…\)
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.