An error of Graphing Calculator Desmos?

Question

Can someone explain to me this error of the Desmos graphic calculator? Why ? For other values of $x$, the exact value of $f(x)$ is obtained.

Or am I wrong when I assure that $f(\sqrt2)=0$?

Answer 1

Almost all software uses certain limited precision. The value shown is very close to being zero. This non-exact value is always to be expected in machine numerical calculations. It happens either due to the methods used in calculating square root, floating point arithmetic in the computer, truncation errors, and so on. Also, this occurs with numbers such as $\pi$, $\sqrt{2}$, etc. See for example How to calculate Square Roots

In short we can't say its wrong, its just that your expectations are high.

Update: It is possible in programming to do something like this:

if variable < tinyConstantValue then
{display zero}
else
{display variable value as is} 

That is to say, we can't tell about how internally the variable value was calculated even though we can see a zero in the result.

A famous reference about floating point in computers is What Every Computer Scientist Should Know About Floating-Point Arithmetic.