Calculate the the given limit$,$ if it exists. $($If an answer does not exist, enter DNE.$)$

lim$$x$$$$

x$6+2,000$x$3+2,000,0006$x$6+3,000$x$3$

If the limit does not exist, say why. $($If the limit does exist, so state.$)$

The limit does exist because it approaches or $$$.$The limit does not exist because the function is not defined for large positive values of x$.$The limit does not exist because the function is not defined for large negative values of x$.$The limit does not exist because it diverges to or $$$.$The limit does exist and is a finite number.