Limiting value of a function

Given a function $f(x)$. If the independent variable $x$ takes on any series of values such that

$$\lim x = a,$$

and at the same time the dependent variable $f(x)$ takes on a series of corresponding values such that

$$\lim f(x) = A,$$

then as a single statement this is written

$$\lim_{x \to a} f(x) = A.$$

Here is an example of a limit using Sage:

[fontsize=\scriptsize,fontfamily=courier,fontshape=tt,frame=single,label=\sage]

sage: limit((x^2+1)/(2+x+3*x^2),x=infinity)
1/3

This tells us that $\lim_{x \to \infty} \frac{x^2+1}{2+x+3*x^2}=\frac{1}{3}$.