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
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alculus with Vector Functions - alculus with Vector...

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