*Date:* MATH 1210-4 - Spring 2004

*Note:* Unless stated otherwise, answers without justification
receive *no credit*. Please, *show your work!*

- Use differentials to approximate .
Since is close to , whose square root is , we use the formula

for , , and . Then, since we have

Using the calculator we obtain the value (rounded to five decimal places) .

- An airplane, flying horizontally, at an altitude of 1 mile,
passes directly over an observer. If the constant speed of the
airplane is 600 miles per hour, how fast is its distance from the
observer increasing 1 minute later?
Figure 1 shows the graph where is the distance from the airplane to the observer and is the (horizontal) distance traveled by the airplane from the moment it passed over the observer.

We know that and we want to know one minute after the plane flew over the observer. Since the plane travels miles per minute, we want to know when .

For all times we have the relation , so that, taking derivatives (with respect to time, ) on both sides we get

so that

Now we see that when , , and we obtain

Javier Fernandez 2004-03-22