## Indeterminate Forms

**Indeterminate Forms:**

If f (x) and g (x) are two functions, then we know that

If Then the expression is said ro be have the indeterminant form , at x = 0

If then is said to have indeterminant form Hence the other indeterminant forms are

**Indeterminate Form 0/0:
**

Here we shall give a method called L' Hospital's Rule to evaluate the limits of the expression which take the indeterminant form;

**L's Hospital's Theorem
**

Let f (x) and g (x) be two functions such that

**1**.

**2**. Then

**Proof :** Suppose f (x) and g (x) satiesfy the conditions of Cauchy's mean value theorem in the interval [a,x]. Then we have

where c lies between a and x i.e a

we get;

Hence,

Then this theorem can be extended as follows:

and so on.