Some problems provide the opportunity for more than one mistake.

The Goal

Determine

Mistake 1

Find the mistake:

Need a hint? Look carefully at the red part:

(The notation "l'H" above the equals sign indicates a step at which l'Hôpital's rule is claimed to be used)

Correction 1

Mistake 2

Find the mistake:

Need a hint? Look carefully at the red part:

Explanations

In the first mistake the derivative of the denominator is computed incorrectly.

In the second mistake the substitution to compute the limit is incorrect (perhaps x=0 was substituted).

Take care to do the simple things correctly.