L'Hopital's rule

The  exercise appears under the Differential calculus Math Mission. This exercise introduces the mechanics of L'hopital's rule and uses it various contexts.

Types of Problems
There is one type of problem in this exercise:


 * 1) Find the limit: This problem has a limit that has a real-number solution. The student is expected to use L'hopital's rule to change the limit into an easier limit and then find the solution.Lhr1.png

Strategies
Knowledge of l-hopital's rule, derivatives, and comfort with evaluation would ensure success on this exercise.
 * 1) To apply the rule, if the limit is of indeterminant form (equivalent to 0/0) take the derivative of the numerator and denominator separately (not by quotient rule) and then take the resulting limit.
 * 2) To increase speed, it is not technically necessary to use L-hopital. One could just plug in a number close to the limit value on a calculator. However, this would undermine the spirit of the problem.

Real-life Applications

 * 1) This rule make limits much easier, but it requires the use of derivatives, whose definition involves limits!