# 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:

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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

more

I don't know. Sympy behaves the same:

sage: from sympy import limit, sqrt
sage: from sympy.abc import x
sage: limit(sqrt(x-3), x, 3)
0
sage: limit(sqrt(x-3), x, 3, dir="+")
0
sage: limit(sqrt(x-3), x, 3, dir="-")
0


BTW, I don't quite understand the term "complex plane" and how the square root converges to 0. Where I can read more about it?

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_...