Category: Differential Calculus, Trigonometry
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Evaluate
Solution:
Consider the given equation
Substitute the value of x to the above equation
Since the answer is 00, then it is also another type of Indeterminate Form and it is not accepted as final answer in Mathematics. We know that any number raised to zero power is always equal to one except for zero that why it is also Indeterminate Form. In this type of Indeterminate Form, we cannot use the L'Hopital's Rule because the L'Hopital's Rule is applicable for the Indeterminate Forms like 0/0 and ∞/∞. Since the given equation is exponential equation, let's consider the following procedure
let
Take natural logarithm on both sides of the equation, we have
Substitute the value of x to the above equation
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
Since the Indeterminate Form is ∞/∞, then we can apply the L'Hopital's Rule as follows
Substitute the value of x to the above equation
Take the inverse natural logarithm on both sides of the equation, we have
Therefore,
