Evaluate this limit, if it exists:
lim (7-x)squared - 9 / 4-x
x->4
To evaluate the given limit, we substitute 4 into the expression and simplify.
First, let's substitute x = 4 into the expression (7 - x)^2 - 9 / (4 - x):
lim (7 - x)^2 - 9 / (4 - x) = (7 - 4)^2 - 9 / (4 - 4)
= 3^2 - 9 / 0
At this point, we have an indeterminate form of a fraction with a zero denominator. This means that the limit may not exist, but we need to do further analysis to be sure.
Let's simplify the expression further:
3^2 - 9 / 0 = 9 - 9 / 0
Now, we can see that we have a division by zero, which is undefined. Therefore, the limit does not exist in this case.
In summary, the limit of the given expression as x approaches 4 does not exist because we encountered a division by zero situation.