Determine the infinite limit. lim x→2 3 − x(x − 2)2

To determine the infinite limit of the function as x approaches 2, we first need to simplify the function.

The function is: 3 - x(x - 2)^2

First, let's expand the function:

= 3 - x(x^2 - 4x + 4)

= 3 - x^3 + 4x^2 - 4x

Now, let's find the limit as x approaches 2:

lim (x→2) 3 - x^3 + 4x^2 - 4x

As x approaches 2, the function becomes:

= 3 - 2^3 + 4(2)^2 - 4(2)

= 3 - 8 + 16 - 8

= 3

So, the limit of the function as x approaches 2 is 3.