1.5. Finding Limits http://www.ck12.org
xlim→ 2 x^2 x++x^3 − 6Our inspection of the graph suggests that the function aroundx=2 does not appear to approach a particular value.
Forx> 2 ,the points all lie in the first quadrant and appear to grow very quickly to large positive numbers as we
get close tox= 2 .Alternatively, forx<2 we see that the points all lie in the fourth quadrant and decrease to large
negative numbers. If we inspect actual values very close tox=2 we can see that the values of the function do not
approach a particular value.
x y
1. 999 − 1000
1. 9999 − 10000
2 ERROR
2. 001 1000
2. 0001 10000For this example, we say that limx→ (^2) x 2 x++x^3 − 6 does not exist.
Formal Definition of a Limit
We conclude this lesson with a formal definition of a limit.
Definition: