when do u say that second order partial derivative is continuous
2006-06-09 19:43:53 · 8 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
continuous functions are any function that you can represent it with a single line when you plot it, there is no holes or asymptotes, for example 1/x or tan(x) are not continuous, however x^2, sin(y), any polonomial is continuous..
2006-06-09 19:49:31 · answer #1 · answered by a_ece_99 2 · 0⤊ 0⤋
say, let f(x, y) be a function of the two variables x and y. differentiate f(x, y) with respect to x once, you get the first-order partial derivative f_x (x, y) of f(x, y) with respect to x. if you differentiate f(x, y) with respect to y, you get the first-order partial derivative f_y (x, y) of f(x, y) with respect to y. now, if you re-differentiate these first-order partial derivatives with respect to either x or y, then you get the second-order partial derivatives f_xx, f_xy, f_yx and f_yy. these second-order partial derivatives are also functions. so consider f_xx (x, y). then f_xx (x, y) is continuous at (a, b) if lim \(x, y) --> (a, b) [f_xx (x, y)] = f_xx (a, b), regardless of the manner in which (x, y) approaches (a, b) (i.e. regardless of the manner in which x approaches a or y a approaches b).
2006-06-09 20:19:35 · answer #2 · answered by JoseABDris 2 · 0⤊ 0⤋
If it's a polynomial, it is always continius. All rational funtions are contunious in their domain. If you want to know if it is continuous in a specific point (a,b) [Asumming your working with two variables] you must fin the limit of the fuction as (x,y) aproaches (a,b). If this limit is equal to the function evaluated in (a,b) then the funtion is continuous at that point. Hope it helps. (I'm still in calculus III)
2006-06-09 20:14:06 · answer #3 · answered by azoteman_213 1 · 0⤊ 0⤋
when you take the derivative, multiply by infinity, divide by the whole circumference, and subtract the brain cells you lost reading this.
2006-06-09 19:48:28 · answer #4 · answered by ohiomandi26 3 · 0⤊ 0⤋
You make no sense at all. Learn how to ask a question correctly and then try again.
2006-06-09 19:46:25 · answer #5 · answered by DiRTy D 5 · 0⤊ 0⤋
Here's a link, with other relevant links:
http://mathworld.wolfram.com/MixedPartialDerivative.html
2006-06-09 20:04:01 · answer #6 · answered by Jimbo 5 · 0⤊ 0⤋
When it satisfies the conditions.
2006-06-09 19:47:06 · answer #7 · answered by ag_iitkgp 7 · 0⤊ 0⤋
when it never equals infinity.
2006-06-09 19:46:10 · answer #8 · answered by arsenic 3 · 0⤊ 0⤋