# Unexpected result in calculating limits

Limit of `sqrt(x-3)`

when `x`

approaches `3`

doesn't exist but the sage returns `0`

. Why is that?

```
sage:
sage: limit(sqrt(x-3), x=3)
0
sage:
```

Unexpected result in calculating limits

Limit of `sqrt(x-3)`

when `x`

approaches `3`

doesn't exist but the sage returns `0`

. Why is that?

```
sage:
sage: limit(sqrt(x-3), x=3)
0
sage:
```

add a comment

1

Maybe because the square root function is defined for negative numbers and the square root of small negative numbers converges to zero as well (on the Complex plane):

```
sage: sqrt(-.00000001)
0.000100000000000000*I
```

1

You may learn about the complex plane here https://en.wikipedia.org/wiki/Complex... and there is a section on the square root of negative number in the wikipedia page of the square root: https://en.wikipedia.org/wiki/Square_...

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Asked: ** 2020-04-15 13:43:24 +0200 **

Seen: **241 times**

Last updated: **Apr 15 '20**

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