Math 237. Calculus II
Exam 1 (noncalculator portion)
Fall, 2011
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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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 Fall '1
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 Calculus, Derivative, Rectangle, indeterminate form ∞/∞

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