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Unformatted text preview: 13.3 Arc Length and Curvature The curvature of a curve can be defined several ways Be able to re-parameterize a curve in terms of the arc length parameter o = + + st 0tdxdu2 dydu2 dzdu2du o Do the integral, and solve t in terms of s, then substitute into r(t) The curvature can be determined by all of the following ways o = = ( ) ( )= ( ) ( ) t dTds T' t r' t r't x r'' t r' t 3 o I t may be hard to memorize, but t ry and think of it as steps o The individual steps are not hard to calculate, just take it one step at a time o Remember you must calculate the derivatives before plugging in the point, however after that it may simplify calculation to plug in for t after that o = ( ) + ( ) / x f'' x 1 f' x 23 2 o Dont worry too much about this formula, but you may want to look at a couple of examples. Extra Exercises: pg 869 #19, #21, #23, o 14.1-Functions of Several Variables Remember how to solve for the domain of a function. I ts the same way as in calc 1 just with more than two variables. Recall the definition of level curves, on pg 892 Extra Exercises: pg 898 #7, #13, #19, #23, #25 o 14.2-Limits and Continuity I t is no longer enough to say a limit exists if you approach it from the left and the right You must prove that it will be the same for any path into some point (x,y) The limit laws still exist as in calculus 1, including the squeeze theorem Also to show that a limit doesnt exist, all you need to find is two paths that...
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- Spring '08
- Arc Length