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 n^th root of a function “f” is the n^th root of the limit of the function.

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

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