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 $\left (x\rightarrow \infty \right )$ , maka berlakulah sifat-sifat berikut:

$\begin{array}{ll}\\ 1.&\underset{x\rightarrow \infty }{\textrm{lim}}\: \displaystyle \frac{1}{x}=0\: \: \textbf{dan}\: \: \underset{x\rightarrow -\infty }{\textrm{lim}}\: \displaystyle \frac{1}{x}=0\\ 2.&\underset{x\rightarrow \infty }{\textrm{lim}}\: \displaystyle \frac{1}{x^{n}}=0\: \: \textbf{dan}\: \: \underset{x\rightarrow -\infty }{\textrm{lim}}\: \displaystyle \frac{1}{x^{n}}=0\\ 3.&\underset{x\rightarrow \infty }{\textrm{lim}}\: k=k\\ 4.&\underset{x\rightarrow \infty }{\textrm{lim}}\: k.f(x)=k.\underset{x\rightarrow \infty }{\textrm{lim}}\: f(x)\\ 5.&\underset{x\rightarrow \infty }{\textrm{lim}}\: \left ( f(x)+g(x) \right )=\underset{x\rightarrow \infty }{\textrm{lim}}\: f(x)+\underset{x\rightarrow \infty }{\textrm{lim}}\: g(x)\\ 6.&\underset{x\rightarrow \infty }{\textrm{lim}}\: \left ( f(x)-g(x) \right )=\underset{x\rightarrow \infty }{\textrm{lim}}\: f(x)-\underset{x\rightarrow \infty }{\textrm{lim}}\: g(x)\\ 7.&\underset{x\rightarrow \infty }{\textrm{lim}}\: \left ( f(x)\times g(x) \right )=\underset{x\rightarrow \infty }{\textrm{lim}}\: f(x)\times \underset{x\rightarrow \infty }{\textrm{lim}}\: g(x)\\ 8.&\underset{x\rightarrow \infty }{\textrm{lim}}\: \displaystyle \frac{f(x)}{g(x)}=\displaystyle \frac{\underset{x\rightarrow \infty }{\textrm{lim}}\: f(x)}{\underset{x\rightarrow \infty }{\textrm{lim}}\: g(x)}\\ 9.&\underset{x\rightarrow \infty }{\textrm{lim}}\: \left (f(x) \right )^{n}= \left [\underset{x\rightarrow \infty }{\textrm{lim}}\: f(x)) \right ]^{n}\\ 10.&\underset{x\rightarrow \infty }{\textrm{lim}}\: \sqrt[n]{f(x)}=\sqrt[n]{\underset{x\rightarrow \infty}{\textrm{lim}}\: f(x)},\quad \textrm{dengan}\: \: \underset{x\rightarrow \infty }{\textrm{lim}}\: f(x)\geq 0 \end{array}$