Use L'Hopital's Rule to evaluate the limit of F(x) as x approaches 0: F(x) = (e2x - 1) / x?

Answer 1

L'Hopital's Rule tells us to take the derivative of the numerator, divide by the derivative of the denominator, and take the limit of that quotient as x goes to 0. So let's do that.

The derivative of the numerator is 2e^(2x) - 0.
The derivative of the denominator is just 1.

So the quotient is 2e^(2x).

The limit of that is 2.

So that's also the value of the limit originally asked for.

Answer 2

2, after you take the derivative, the e^(2x) turns to 1.