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Saturday, June 1, 2013

Indeterminate Form - Zero Over Zero, 3

Category: Differential Calculus, Algebra

"Published in Suisun City, California, USA"

Evaluate


Solution:

Consider the given equation above



Substitute the value of x which is 0 to the above equation, we have



Since the answer is 0/0, then it is considered as Indeterminate Form which is not accepted as a final answer in Mathematics. Remember this, any number, except zero divided by zero is always equal to infinity. If the Indeterminate form is either 0/0 or /, then we can use the L'Hopital's Rule in order to solve for these type of Indeterminate Forms. In this case, we can apply the L'Hopital's Rule for the above equation as follows



 

Substitute the value of x which is 0 to the above equation, we have


Since the answer is again 0/0, then we have to apply again the L'Hopital's Rule, as follows






Substitute the value of x which is 0 to the above equation, we have


Since the answer is again 0/0, then we have to apply again the L'Hopital's Rule, as follows




Substitute the value of x which is 0 to the above equation, we have


Therefore,