# Basic properties or theorems of limit.

The limit theorems or basic properties of limit are given below:

1> The limit of the sum (or difference) of the functions “f” and “g” is the sum (or difference) of the limits of the functions

i.e.

$\displaystyle\lim_{x\to a}[f(x) \pm g(x)]=\displaystyle\lim_{x\to a}f(x)\pm\displaystyle\lim_{x\to a}g(x)$

2> The limit of the product of the function “f” and “g” is the product of the limits of the functions.

i.e.

$\displaystyle\lim_{x\to a}[f(x).g(x)]=\left(\displaystyle\lim_{x\to a}f(x)\right).\left(\displaystyle\lim_{x\to a}g(x)\right)$

3> The limit of the quotient of the function “f” and “g” is the quotient of the limits of the functions.

i.e.
$\displaystyle\lim_{x\to a}\frac{f(x)}{g(x)} =\frac{\displaystyle\lim_{x\to a}f(x)}{\displaystyle\lim_{x\to a}g(x)}$

4> The limit of nth root of a function “f” is the nth root of the limit of the function.

i.e.
$\displaystyle\lim_{x\to a}\sqrt[n]{f(x)}=\sqrt[n]{\displaystyle\lim_{x\to a}f(x)}$

Related posts:

1. Right hand and Left hand limit of a function. The limit of a function have two categories : Left...
2. The concept of Limit. Limit of a function is the value to which function...
3. Basic properties of Logarithms. Logarithms are important throughout mathematics and science. Establishing some basic...
4. The Logarithmic Function. There are many ways to describe logarithmic function. One basic...
5. Composite Function. A single function formed by the combination of two or...