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L'hopital rule

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I can't seem to grasp the concept of L'Hopital's Rule. How do you know whether to use it or not in evaluating a limit? If anyone could answer this and give me a step by step example for how to solve this that would be extremely helpful (the more complicated the example, the better, since the examples on our tests will be very challenging).

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Solution Summary

The 6 pages solution shows how to utilize L'hopital rule and what are the conditions required for its application.
there are 5 examples that demonstrate different tricks and properties of the rule.

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