Limit of a Function at a Point

The limit of the function, f(x), at point, x0,
is essentially the value of y when x approaches x0.

Take for example, the function f(x) = x² at the point x0 = 2.

x f(x)
1,9 3,61
1,99 3,9601
1,999 3,996001
... ...
2 4
x f(x)
2,1 4.41
2,01 4,0401
2,001 4,004001
... ...
2 4

When x becomes closer to 2 from the left and right side the value of the function will approach 4.

It is said that the limit of the function, f(x) , as x tends to x0, is L. If a real positive number is set, ε, greater than zero, there will be a positive number, δ, depending on ε , for all the values of x that differ from x0 that fulfill the condition |x - x0| < δ , and holds that |f(x) - L| <ε .

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