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alculus with Vector Functions

# alculus with Vector Functions - alculus with Vector...

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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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Notice 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 it clear here are some facts about derivatives of vector functions.
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