Continuity Theorems.


Posted in Limits and Continuity., Mathematics




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.



Related posts:

  1. Basic properties or theorems of limit. Four basic properties of limits of a function or limit...
  2. Continuity of a function(continuous and discontinuous functions). Continuity of a function , a function can either be...
  3. Exponent(index) and laws of exponents(indices). When , a number is repeatedly multiplied by itself the...
  4. Basic properties of Logarithms. Logarithms are important throughout mathematics and science. Establishing some basic...
  5. The concept of Limit. Limit of a function is the value to which function...