Quiz 6 is here.
Problem 1 defines a function by , and asks to compute .
First, we find . For this, we use the chain rule, recalling that .
We have . Thus .
Problem 2 asks to compute .
Note that , so we can try to use L’Hôpital’s rule to compute the required limit: L’Hôpital’s rule tells us that if is a number or , and
- , and
as well. (There is a similar version when
but we do not need it here.)
In our case, condition 1 holds. As for condition 2, we see that
and therefore .
It follows that
The graph of , shown below, seems to confirm our computations.
Click the image above to enlarge.