I read an article stating that GPU are the future of supercomputing. I would like to know what are the programming languages used for programming on GPU's


Question: Why is the limit of this root the absolute value
Answer: Note that $h_{n}(x)=x\cdot x^{1/(2n-1)}$, and since $n$ is a natural number, this is an odd root of $x$. In particular, it preserves the sign, since $$(-x)^{1/r}=-x^{1/r}$$
is true iff $r$ is odd (for a proof, raise both sides to the power $r$).
So when $x\ge0$ you have seen the result is obviously true, and if $x&lt;0$ we can apply the above result.