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You are not logged in. #1 20060208 14:14:08
continuity of parametric equationsyou can only integrate using the arc length formula to find the length of a curve if the curve is continuous on the given interval. If their is a sharp point at b between a and c, you need to integrate from a to b, then b to c. a to c won't work since the function must be continuous to integrate. Last edited by mikau (20060208 14:15:20) A logarithm is just a misspelled algorithm. #2 20060208 14:24:02
Re: continuity of parametric equationsYou want differentiability, not continuity. I'm still working on this problem though. "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #3 20060208 14:55:12
Re: continuity of parametric equationsDoesn't continuity imply differentiability? A logarithm is just a misspelled algorithm. #4 20060208 15:02:31
Re: continuity of parametric equationsIf a function is differentiable, then it is continuous. But consider the function f(x) = x. It is continuous at 0, but not differentiable. "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #6 20060208 15:19:18
Re: continuity of parametric equationsf(t) = ( 4 cos(t)  4 cos(4t) , 4 sin (t)  4 sin(4t) ) where Df(x0) is the matrix of partial derivatives. In this case: Df = ( 16sin(4t)  4sin(t) , 4cos(t)  16cos(4t) ) Since there is only one variable in this function, there are no partials. Try using that definition to see if it works. "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #7 20060208 15:23:08
Re: continuity of parametric equationsI'm not sure what you mean. That must be above my level. This is calculus 1. I have no idea what "matrix of partial derivative" is. Last edited by mikau (20060208 15:23:45) A logarithm is just a misspelled algorithm. #8 20060208 15:31:42
Re: continuity of parametric equationsIf you can use a graphing calculator, you can spot nondifferentiable parts at a point if: "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #9 20060208 15:34:38
Re: continuity of parametric equationsSo you can spot it on a graphing calculator if it has a corner point or cusp? A logarithm is just a misspelled algorithm. #10 20060208 15:58:42
Re: continuity of parametric equationsThis is the drawback of being self taught. When your stuck you can't ask teacher. Last edited by mikau (20060208 15:59:53) A logarithm is just a misspelled algorithm. 