Limit di Ketakhinggaan (Kelas XII Matematika Peminatan)

 Untuk $n$ bilangan bulat positif, dan $k$ suatu konstanta, serta fungsi  $f$ dan $g$ adalah dua buah fungsi yang memiliki nilai limit saat  $x$  mendekati ketakhinggaan $(x\to \mathrm{\infty })$ , maka berlakulah sifat-sifat berikut:

$\begin{array}{l}\\ 1.& \underset{x\to \mathrm{\infty }}{\text{lim}}{\displaystyle \frac{1}{x}=0\mathbf{\text{dan}}\underset{x\to -\mathrm{\infty }}{\text{lim}}{\displaystyle \frac{1}{x}=0}}\\ 2.& \underset{x\to \mathrm{\infty }}{\text{lim}}{\displaystyle \frac{1}{x^n}=0\mathbf{\text{dan}}\underset{x\to -\mathrm{\infty }}{\text{lim}}{\displaystyle \frac{1}{x^n}=0}}\\ 3.& \underset{x\to \mathrm{\infty }}{\text{lim}}k=k\\ 4.& \underset{x\to \mathrm{\infty }}{\text{lim}}k.f(x)=k.\underset{x\to \mathrm{\infty }}{\text{lim}}f(x)\\ 5.& \underset{x\to \mathrm{\infty }}{\text{lim}}(f(x)+g(x))=\underset{x\to \mathrm{\infty }}{\text{lim}}f(x)+\underset{x\to \mathrm{\infty }}{\text{lim}}g(x)\\ 6.& \underset{x\to \mathrm{\infty }}{\text{lim}}(f(x)-g(x))=\underset{x\to \mathrm{\infty }}{\text{lim}}f(x)-\underset{x\to \mathrm{\infty }}{\text{lim}}g(x)\\ 7.& \underset{x\to \mathrm{\infty }}{\text{lim}}(f(x)\times g(x))=\underset{x\to \mathrm{\infty }}{\text{lim}}f(x)\times \underset{x\to \mathrm{\infty }}{\text{lim}}g(x)\\ 8.& \underset{x\to \mathrm{\infty }}{\text{lim}}{\displaystyle \frac{f(x)}{g(x)}={\displaystyle \frac{\underset{x\to \mathrm{\infty }}{\text{lim}}f(x)}{\underset{x\to \mathrm{\infty }}{\text{lim}}g(x)}}}\\ 9.& \underset{x\to \mathrm{\infty }}{\text{lim}}{(f(x))}^n={[\underset{x\to \mathrm{\infty }}{\text{lim}}f(x))]}^n\\ 10.& \underset{x\to \mathrm{\infty }}{\text{lim}}\sqrt[n]{f(x)}=\sqrt[n]{\underset{x\to \mathrm{\infty }}{\text{lim}}f(x)},\text{dengan}\underset{x\to \mathrm{\infty }}{\text{lim}}f(x)\ge 0\end{array}$