Applying L'Hôpital's Rule

Question

Consider the function defined by $$f(x)=\frac{e^{2*x} - 1}{x}$$. All of the following statements about the limit $$\lim_{x	o 0} f(x)$$ are true except:

Accepted Answer

The limit equals 0.

Answer

Applying L'Hôpital's rule is appropriate since the limit is in an indeterminate form.

Answer

Evaluating the derivatives at $$x=0$$ yields $$2*e^0 = 2$$, which is the limit.

Answer

Differentiating the numerator gives $$2*e^{2*x}$$ and the derivative of the denominator is 1.