- #1
imana41
- 36
- 0
please say is it this limit available on (0,0)
lim((x^2*y^2)/(x^2+y^2))
thanks
lim((x^2*y^2)/(x^2+y^2))
thanks
Char. Limit said:What have you tried. Try taking the limit across x=0, y=0, and y=x, for the most common limits.
Kreizhn said:Whoa, are you sure all the limits are zero? You have to do some work yourself before we can help.
Kreizhn said:Well, if you try all the trajectories that Char. Limit gives, yes, they will all go to zero, but it would be nice to see that you've done some of the work there.
However, just because the limit from 3-paths are consistent doesn't mean that the limit exists. You need to apply stronger techniques. In particular, this problem is probably best handled by converting it to polar coordinates and examining the case when the radial coordinate tends to zero.
Metaleer said:imana41, I don't think you quite understand how this forum works. You're supposed to show us your work so that we know where you're stuck and so that we can give you a push in the right direction. We aren't homework help robots.
A two variable limit refers to the limit of a function that has two independent variables. It is the value that the function approaches as both variables approach a certain point.
A two variable limit is calculated by taking the limit of the function as each variable approaches the specified point separately, and then combining the results to determine the overall limit.
When a two variable limit is "0,0" available, it means that the limit of the function as both variables approach 0 is equal to 0. This can also be written as lim f(x,y) = 0 as (x,y) → (0,0).
The concept of a two variable limit is important in science because it allows us to understand the behavior of functions with multiple independent variables. It is especially useful in fields such as physics, where multiple variables may affect the outcome of a phenomenon.
Yes, there are many real-life applications of two variable limits. For example, in economics, it can be used to calculate the marginal rate of substitution between two goods. In engineering, it is used to optimize processes and designs. It is also commonly used in physics and chemistry to model and analyze systems with multiple variables.