## Thursday, June 26, 2014

### Indeterminate Form - Combined, 2

Category: Differential Calculus, Algebra

"Published in Newark, California, USA"

Evaluate

Solution:

To get the value of a given function, let's substitute the value of n to the above equation, we have

Since the answer is (∞ - ∞)/∞ , then it is an Indeterminate Form which is not accepted as a final answer in Mathematics. We cannot use the L'Hopital's Rule because the Indeterminate form is (∞ - ∞)/∞. L'Hopital's Rule is applicable if the Indeterminate Form is either 0/0 or ∞/∞. We have to do something first in the given equation so that the Indeterminate Form becomes 0/0 or ∞/∞.

Let's rewrite the above equation by expanding and simplifying the numerator as follows

Substitute the value of n to the above equation, we have

Since the Indeterminate Form is  ∞/∞, then we can use the L'Hopital's Rule to the above equation as follows

Since the variables at the right side of the equation are all canceled, then there's no other way to substitute the value of a variable to the right side of the equation.

Therefore,