"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 Indeterminate Form is ∞/∞, then we can use the L'Hopital's Rule but the problem is there's an exponent that associated with the Indeterminate Form. We have to eliminate the exponent first before we can apply the L'Hopital's Rule to the given equation. We cannot accept as a final answer for the given equation.
Let
Take natural logarithm on both sides of the equation
Since the Indeterminate Form is ∞/∞, then we can use the L'Hopital's Rule but the problem is the Indeterminate Form is a function of natural logarithm. We have to rewrite the above equation as follows
Divide both the numerator and denominator by 1/x, we have
Substitute the value of x to the above equation, we have
Since the Indeterminate Form is ∞∙0, then we have to rewrite the above equation as follows
Substitute the value of x to the above equation, we have
Since the Indeterminate Form is 0/0, then we can use the L'Hopital's Rule as follows
Substitute the value of x to the above equation, we have
Take the inverse natural logarithm on both sides of the equation
Therefore,
