it would be much easier if u wrote it like
and then apply it
I tried solving the following problem many times, but each time I do I end up with the wrong answer. Is the order which I differentiated this expression in correct? Also, is the derivative of e (a constant) e or 0? I'm still very new to calculus, so I'd really appreciate a detailed explanation in regarsds to solving this problem. Thanks.
After applying the quotient rule, I ended up with:
In order to simplify, is it necessary that I find the derivatives of the expressions accompanied by the prime notation? Or do I ignore the primes and begin by converting this one fraction into two of them?
You are making things complicated for yourself.
L'Hopital's rule is used when the limit of your right-hand factor
approaches as n goes to infinity.
It's already in that form, but the differentiation wrt n is inconvenient due to
n being in a denominator position.
Therefore substitute and evaluate the limit as x goes to zero instead.
Now differentiate numerator and denominator since you still have
if you try to evaluate the limit.
Use the product rule for the numerator.
Correct me if I'm wrong, but I believe there's a problem here. The top, tends towards 1 as , whereas the bottom is the indeterminate form as ?
Let's rewrite the limit as
We need to evaluate the bottom first. Change it to
Applying L'Hopital's rule,
.
Which simplifies to .
and so our solution is ?
Math Major, the answer to this problem can be found at Solutions to the Limit Definition of a Definite Integral . The problem was that I didn't understand anything past the L'Hopital's Rule point.