# Question #1488e

##### 1 Answer

The limit does not exist.

#### Explanation:

We can't simply plug in

However, note that at

Instead, it will be

Let's approach

Let

#x = 2 + a# , where#a# is an extremely small number. Then the negative limit is:

#lim_(a->0^-)((2+a)^(1/3)-2)/a = "negative value"/"negative value approaching 0" = "positive value"/"positive value approaching 0" = oo# Similarly, the positive limit is:

#lim_(a->0^+)((2+a)^(1/3)-2)/a = "negative value"/"positive value approaching 0" = -oo#

Since the negative limit is

To show this limit, here is the graph of the function

graph{(x^(1/3)-2)/(x-2) [-3.184, 6.816, -2.32, 2.68]}

*Final Answer*