Final answer:
The limit of ( | x-3 |)/(x - 3) as x approaches 3 from the left is -1, due to the negative value within the absolute value when x is less than 3.
Step-by-step explanation:
The question asks for the limit of the function ( | x-3 |)/(x - 3) as x approaches 3 from the left (x → 3-). To solve this, we consider the definition of absolute value. When x is less than 3, x - 3 is negative, so | x-3 | is equal to -(x-3). Therefore, the function becomes (-(x-3))/(x-3) which simplifies to -1. As x approaches 3 from the left, the function remains equal to -1. Thus, the limit is -1.
The given problem is evaluating the limit of a function as x approaches 3-. The function is |x-3|/(x - 3).
To evaluate the limit, we need to consider the left-hand side limit, lim (|x-3|)/(x - 3) as x approaches 3-.
When x approaches 3-, x-3 becomes negative. So, |x-3| simplifies to -(x-3). The function becomes -(x-3)/(x-3). Canceling out the common factor of (x-3) yields -1.
Therefore, the value of the given limit is -1.