# Continuity Theorems.

The basic theorems based on continuity are given below:

If the functions f(x) and g(x) are continuous at x=a then,

1> $f(x) \pm g(x)$ is continuous at x=a.

2>$f(x) \times g(x)$ is continuous at x=a.

3>$\cfrac{f(x)}{g(x)}$ is continuous at x=a , if g(x) is not equal to 0.

4>$\sqrt[n]{f(x)}$ is continuous at x=a if f(x) is greater than 0 , or is a positive number when “n” is even.

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