alculus with Vector Functions
In this section we need to talk briefly about limits, derivatives and integrals of vector
functions. As you will see, these behave in a fairly predictable manner. We will be
doing all of the work in
but we can naturally extend the formulas/work in this
section to
(
i.e.
n
dimensional space).
Let’s start with limits. Here is the limit of a vector function.
So, all that we do is take the limit of each of the components functions and leave it as
a vector.
Example 1
Compute
where
.
Solution
There really isn’t all that much to do here.
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View Full DocumentNotice that we had to use
L’Hospital’s Rule
on the
y
component.
Now let’s take care of derivatives and after seeing how limits work it shouldn’t be too
surprising that we have the following for derivatives.
Example 2
Compute
for
.
Solution
There really isn’t too much to this problem other than taking the derivatives.
Most of the basic facts that we know about derivatives still hold however, just to make
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 Fall '08
 prellis
 Derivative, Integrals, Limits

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