Exam 1 solutions (non-calculator portion)

Exam 1 solutions (non-calculator portion) - Math 237...

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Math 237. Calculus II Exam 1 (non-calculator portion) Fall, 2011 Name: Solutions Evaluate the following limits. This has the indeterminate form ∞/∞, so L'Hôpital's rule applies. This also has the indeterminate form ∞/∞, but using L'Hôpital's rule at this point leads nowhere. So I simplified. (Getting this far was worth 6 points.) This last limit has the indeterminate form 0/0, so L'Hôpital's rule applies again. = 0 Let . Then . And That last limit has the indeterminate form ∞/∞, so L'Hôpital's rule applies. The last of those limits has the indeterminate form 0/0, so L'Hôpital's rule applies again. Since , then .
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Find derivatives for the following. 3. Starting off applying the product rule gives 4. Starting off by applying the quotient rule gives Find the following integrals. Getting this one is mainly a matter of recognition. Getting this one is mainly a matter of recognition, too. For this one I'll make the substitution . This gives . So
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