## Friday, June 27, 2014

### Indeterminate Form - Zero Over Zero, 7

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 x to the above equation, we have

Since the answer is 0/0, then it is an Indeterminate Form which is not accepted as a final answer in Mathematics. We have to do something first in the given equation so that the final answer will be a real number, rational, or irrational number.

Method 1:

Since the answer is Indeterminate Form, then we have to factor the numerator and denominator if they can and then simplify as follows

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

Therefore,

Method 2:

Another method of solving Indeterminate Form is by using L'Hopital's Rule. This is the better method especially if the rational functions cannot be factored. L'Hopitals Rule is applicable if the Indeterminate Form is either 0/0 or ∞/∞. Let's apply the L'Hopital's Rule to the given function by taking the derivative of numerator and denominator with respect to x as follows

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

Therefore,