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A limit is the intended height of a function at a given value of x, whether or not the function actually reaches that height at the given x. In the case of f, you know that f does reach the value of 11 when x = 3, but that doesnât have to be the case for a limit to exist.hat Limit Means. Letâs start with a simple function: f(x) = 2 x + 5. You know that this is a line with slope 2 and y-intercept 5. If you plug x = 3 into the function, the output will be f (3) = 2 Â· 3 + 5 = 11.