Common Calculus Mistakes
Example: l'Hôpital's Rule 
Some problems provide the opportunity for more than one mistake. The Goal
Determine
The Mistakes
Find the mistakes:
(Roll the mouse over the math to see a hint in red) (Roll the mouse over the math to see a hint in red) A Correct Solution
(Roll the mouse over the area above to see the corrections in blue) Explanations
In the first mistake the student has misunderstood l'Hôpital's rule to apply to a product. L'Hôpital's rule can be used to find the limit of a quotient when both the numerator and denominator are differentiable on an open interval containing the point of interest (or on an infinite open interval if the limit is to be taken at ±∞) and when the limit has indeterminate form, that is, the numerator and denominator both approach zero in the limit or each approaches either ∞ or ∞. Thus the first step is to rearrange the limit expression into the form of an indeterminate quotient. 
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