Evaluate the limit, if it exists. (If it does not exist, enter NONE).

lim h→0 (3 + h)3 − 27
_______________
h

To evaluate the limit of this expression, let's simplify it step by step.

First, let's substitute h = 0 into the expression:

lim h→0 (3 + h)^3 - 27
_______________
h

This simplifies to:

(3 + 0)^3 - 27
____________
0

Simplifying further:

(3)^3 - 27
_________
0

= 27 - 27
_______
0

= 0
___

Since we obtained a finite value of 0, the limit exists, and the value of the limit is 0.

To evaluate the limit, we can substitute the value of h equal to 0 into the expression and simplify. Let's go step by step:

1. Substitute h = 0 into the expression:
(3 + 0)^3 - 27
Simplify:
3^3 - 27

2. Evaluate the expression:
3^3 = 27, so we have:
27 - 27 = 0

3. Since the numerator is 0, we need to check the denominator. If the denominator is also 0, then the limit does not exist. Let's check the denominator:
h

4. Substitute h = 0 into the denominator:
0

5. The denominator is also 0, which means the limit does not exist.

Therefore, the limit of the given expression as h approaches 0 does not exist.