## Saturday, December 29, 2012

### Indeterminate Form - One Raised Infinity

Category: Differential Calculus

"Published in Newark, California, USA"

Evaluate

Solution:

Consider the given equation

Substitute the value of x to the above equation

One raised to infinity is also another type of Indeterminate Form and it is not accepted as a final answer in Mathematics. We know that one raised to any number is always equal to one but in this case, one raised to infinity is not always equal to one, that's why 1 is also an Indeterminate Form. In this type of Indeterminate Form, we cannot use the L'Hopital's Rule because the L'Hopital's Rule is applicable for the Indeterminate Forms like 0/0 and ∞/∞. Since the above equation involves exponential function, we can rewrite the equation as follows

let

Take natural logarithm on both sides of the equation

Substitute the value of x to the above equation

Since the Indeterminate Form is ∞∙0, we have to rewrite the equation again as follows

Substitute the value of x to the above equation

Since the Indeterminate Form is 0/0, then we can now use the L'Hopital's Rule as follows

Substitute the value of x to the above equation

Take inverse natural logarithm on both sides of the equation

Therefore,