First, check that the table is in standard form, with x-values less than -5 on the left, and x-values greater than -5 on the right. It is already in standard form:

x approaching -5 from the left		x approaching -5 from the right
x -5.1 -5.01 -5.001 -5.0001 g(x) 23.2 23.1 23.001 23.0001	-5 24	-4.9999 -4.999 -4.99 -4.9 249999.9 24999.9 249.9 24.9

This table gives us the following information:

As x approaches -5 from the left, g(x) approaches 23. In other words,

lim   x-5

g(x) = 23

Note The fact that you see the number 24 under x = -5 means that g(-5) = 24. That is, the value of g at -5 is 24. When taking the limit as x approaches -5, ignore the value of the function at x = -5. The limit is about what happens as x approaches -5, not what happens when x equals -5.

As x approaches -5 from the right, g(x) becomes very large, and is therefore approaching infinity. Therefore,

lim   x-5

g(x) = +∞.       Some people say that it doesn't exist when this happens...

Since the left- and right-hand limits do not agree there is no hope of the lim_{x → -5} g(x) existing. In other words,

lim   x-5

g(x) does not exist.

Finally, the value of the function at x = -5 is given by the table:

g(-5) = 24.

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