Various Indeterminate Forms

Indeterminate Forms ∞ – ∞ and 0 × ∞:

L' Hospital rule can be applied to limits which take the indeterminant forms First we transform the given limit in the form of

and then by use L' Hospital rule to evaluate the limits.

Indeterminate Forms 00, 1∞, ∞0, 0∞:

Let If L takes one of the indeterminant form then taking logarithm on both side we get;

The Log L will take the indeterminant forms and which can be evaluated by using the method employed in preceding sections.

Examples:

Example1. Evaluate

By L' Hospital Rule;

Ex 2. Evaluate

By L' Hospital Rule;