The given limit can be evaluated using the properties of exponential functions and basic algebraic manipulation. Let's break down the problem into steps to find the limit as x approaches 1 of the given expression:

Step 1: Rewrite the expression in a simplified form
The given expression is 4^x * (1 - 4/2x). To simplify this expression, we can start by simplifying the fraction 4/2x:

4/2x = 2/x

Now, our expression becomes 4^x * (1 - 2/x).

Step 2: Simplify the expression further
To simplify the expression even more, we can multiply the terms inside the parentheses by a common denominator, which is x:

(1 - 2/x) = (x/x - 2/x) = (x - 2)/x

Now, our expression becomes 4^x * (x - 2)/x.

Step 3: Evaluate the limit
To find the limit as x approaches 1, we substitute x = 1 into the expression:

lim(x→1) 4^x * (x - 2)/x

Plugging in x = 1, we get:

4^1 * (1 - 2)/1 = 4 * (-1) = -4

Therefore, the limit as x approaches 1 of the given expression is -4.

Visually appealing breakdown:

Step 1: Rewrite the expression in a simplified form
4^x * (1 - 4/2x)

Step 2: Simplify the expression further
4^x * (1 - 2/x) = 4^x * (x - 2)/x

Step 3: Evaluate the limit
lim(x→1) 4^x * (x - 2)/x = 4^1 * (1 - 2)/1 = 4 * (-1) = -4