"Published in Suisun City, California, USA"
Evaluate
Solution:
Consider the given equation above
Substitute the value of x to the above equation, we have
Since the answer is 0/0, then it is Indeterminate Form that is not accepted as a final answer in Mathematics. We have to do something first in the equation above so that the final answer is a real number and not indeterminate form.
There are two ways in solving the value of the limit for the above equation. Let's consider the two ways in solving the limits.
Method 1:
Since the indexes of the radicals at the above equation are different, then we have to convert them the same indexes as follows:
Let
If x = 1, then y will be equal to
Substitute the value of y to the above equation, we have
Since the answer is 0/0 again, then it is Indeterminate Form also that is not accepted as a final answer in Mathematics. We have to do something in the equation above so that the final answer is a real number and not indeterminate form.
Since the numerator and the denominator can now be factored, then the above equation becomes
Substitute the value of y to the above equation, we have
Therefore,
Method 2:
There's another way in solving the limits which is called the L'Hopital's Rule. L'Hopital's Rule is applicable if the Indeterminate Form is either 0/0 or ∞/∞. Consider again the given equation, we have
Apply the L'Hopital's Rule to the above equation, we have
Substitute the value of x to the above equation, we have
Therefore,
