How are you taking the limit?
I am looking at the values of y as x approaches 3 using the table function on a Ti-83 graphing calculator.
From the left and right, the function seems to approach -8 at a uniform rate around x=3. Based on what I've been taught so far about limits, that should make the limit -8.
Also, my "understanding" prior to this had been that:
limit = slope of a tangent line = rate of change = derivative
I've got it:
Not all limits are derivatives, but all derivatives are limits.
In other words, the derivative is a specific kind
of limit (using, in one form, the difference quotient).
If I've got this right, then I sure wish textbook authors would see the value of pointing stuff like this out to thick-headed folks like myself.