explain limit as x approaches infinity?

This limit says that the graphs of y=G(x) and y=x become nearly identical for large values of x (and more nearly, the larger x gets). The geometric term for this is "asymptotic", and the line graphed by y=x is an "asymptote" of the curve graphed by y=G(x).

So, just sketch a graph that starts out however you like near the origin but homes in on the y=x line off to the right. If you have a graphing calculator, try these for some ideas:

G(x) = 1 + 1/x

G(x) = (x^2 - 1)/(x^2 + 1)

G(x) = (x + sin(x))/(x + 1)

drawing close infinity: because the two the numerator and denominator are non-end applications, the fee of the shrink of each is merely the fee of the applications at x = a million that's 0. subsequently, utilising the quotient rule for limits might bring about a nil/0 kind. drawing close damaging infinity: The spinoff of the numerator is 2x + a million whose shrink is 3 as x strategies a million. The spinoff of the denominator is 2x - a million whose shrink is likewise a million as x strategies a million. this gives you a three/a million kind meaning the shrink is 3. i'm assuming that as you're asking this question, which you have some awareness and which you will comprehend this answer.

it means, when x approaches infinity, the f(x) values will approach a value as a possibility.

Can G(x) = | x |

and/ or [ ... ] be the G.I.F.( greatest integer function ?

I need to know what G(x) is !