Let a=8, f(x)=|x-8|/x
You are given lim x->a- f(x)=lim x->8-
|x-8|/x
Is the limit of the value 0.
To determine the limit of the given expression as x approaches a from the left, we substitute a = 8 into the expression and evaluate it.
The expression is: lim x->a- |x-8|/x
Substituting a = 8, we have: lim x->8- |x-8|/x
Now, let's evaluate the expression for x approaching 8 from the left side. When x approaches 8 from the left side, x becomes smaller and smaller but is still greater than 8. Therefore, the expression simplifies as follows:
lim x->8- |x-8|/x = |8-8|/8
Since 8-8 equals 0, and 0 divided by any nonzero number (in this case, 8) is always 0, we have:
lim x->8- |x-8|/x = 0
Therefore, the limit of the given expression as x approaches 8 from the left is 0.