Limits with 3 variables
Favorites|Homepage
Subscriptions | sitemap
HOME > Mathematics > Limits with 3 variables

Limits with 3 variables

[From: ] [author: ] [Date: 11-10-31] [Hit: ]
0,0) for (x^2+2y^2+3z^2)/(x^2+y^2+z^2)-You have continuous partial derivatives all around (but not at) the origin,lim/x->0 f(x, 0,lim/y->0 f(0, y,......
Hi,
can somebody help me with this? The textbook doesn't give any good examples on how to solve these.

lim as (x,y,z) --> (0,0,0) for (x^2+2y^2+3z^2)/(x^2+y^2+z^2)

-
You have continuous partial derivatives all around (but not at) the origin, so the limit will exist if each of the single-variable limits exist and have the same value:

lim/x->0 f(x, 0, 0) = lim x^2 / x^2 = 1
lim/y->0 f(0, y, 0) = (2y^2) / y^2 = 2
lim/z->0 f(0, 0, z) = (3z^2) / z^2 = 3

Approaching (0,0,0) from three different directions gives different results, so the limit does not exist.

-
x-> 0 then y-> 0 then z-> 0

Ans

3
1
keywords: variables,Limits,with,Limits with 3 variables
New
Hot
© 2008-2010 http://www.science-mathematics.com . Program by zplan cms. Theme by wukong .