Category: Differential Calculus, Trigonometry
"Published in Vacaville, 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 apply the double angle formula at the numerator 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,