# Limits of functions of two variables

How to find the limit of a function with two variables at a point (x,y)?

The command limit( f(x), x=a) only works for one-variable function.

Limits of functions of two variables

How to find the limit of a function with two variables at a point (x,y)?

The command limit( f(x), x=a) only works for one-variable function.

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1

If your function is "nice enough", you can try to take the limit one at a time. In general, the limit may not exist.

```
sage: f(x,y) = x^2 + y^2
sage: f.limit(x=0).limit(y=0)
(x, y) |--> 0
sage: f.limit(x=0).limit(y=2)
(x, y) |--> 4
```

Asked: **
2013-12-18 16:13:21 -0600
**

Seen: **920 times**

Last updated: **Dec 23 '13**

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