Chain Rule Error In L'Hôpital's Rule

Question

A student attempts to evaluate the limit $$\lim_{x	o 0} \frac{e^{3*x}-1}{x}$$ using L'Hôpital's rule. However, she mistakenly differentiates $$e^{3*x}$$ as $$e^{3*x}$$ (omitting the chain rule factor) and thus obtains an incorrect limit. Identify the error and determine the correct limit.

Accepted Answer

The error is neglecting the chain rule. The derivative of $$e^{3*x}$$ is $$3*e^{3*x}$$, so the limit becomes 3.

Answer

There is no mistake; the limit is correctly computed as 1.

Answer

She should have recognized that the limit does not exist because of the exponential function.

Answer

The mistake is in differentiating the denominator; it should have been differentiated as 3.