lim |x-3|/x-3
x-->3^-
A) 0 B) -1 C) 1
https://www.mathway.com/popular-problems/Calculus/501103
To find the limit of the given expression, we substitute the value that x is approaching into the expression. In this case, x is approaching 3 from the left side (denoted by the exponent -).
To evaluate the expression, |x-3| / (x-3), when x=3, we start by substituting 3 into the expression:
|(3) - 3| / (3 - 3)
Now simplify:
|0| / 0
The absolute value of 0 is 0:
0 / 0
However, 0 divided by 0 is an indeterminate form. It means that by simply substituting the value of x, we cannot determine the specific value of the limit. We need to approach the problem differently.
To find the limit in this case, we can simplify the expression by canceling out the common factor of (x - 3) in both the numerator and denominator.
|x - 3| / (x - 3) = |1|
Since we have canceled out the (x - 3), we are left with |1|. The absolute value of 1 is simply 1.
Therefore, the limit of the expression as x approaches 3 from the left side (x --> 3^-) is 1.
So, the answer is C) 1.