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Unformatted text preview: Example 2 Determine the arc length function for . Solution From the previous example we know that, The arc length function is then, Okay, just why would we want to do this? Well let’s take the result of the example above and solve it for t . Now, taking this and plugging it into the original vector function and we can reparameterize the function into the form, . For our function this is, So, why would we want to do this? Well with the reparameterization we can now tell where we are on the curve after we’ve traveled a distance of s along the curve. Note as well that we will start the measurement of distance from where we are at . Example 3 Where on the curve are we after traveling for a distance of ? Solution To determine this we need the reparameterization, which we have from above. Then, to determine where we are all that we need to do is plug in into this and we’ll get our location. So, after traveling a distance of along the curve we are at the point ....
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This note was uploaded on 11/10/2011 for the course MATH 136 taught by Professor Prellis during the Fall '08 term at Rutgers.
 Fall '08
 prellis
 Arc Length

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