The linear approximation to a change in the argument of a function f(x) is

So we know that the initial diameter of the tree is d = 10 in. And we know that the circumference of the tree grows by 2 in.

The formula for the circumference is

so

I'm assuming you have to use the linear approximation equation here (though the answer turns out to be exact, not an approximation) so

and

Thus

For the second problem, we know that the cross-section is a circle and the area of a circle is:

So

The change in d is:

So

(The actual area is , so this is a good approximation.)

-Dan