In calculating the limit of a rational fraction, if the denominator does not evaluate to zero, the limit is found be simply substituting the limit of x for x.
If the denominator evaluates to zero, and so does the numerator, we can see if there is a common factor. If there is, we can cancel the common factor and proceed as another rational fraction (or a polynomial).
As x->8, the denominator evaluates to zero, so we check the numerator. The numerator also evaluates to zero.
We note that the numerator factors into (x+8)(x-8), which has a common factor of (x+8) with the denominator.
Cancelling the common factor leaves us with (x-8), which is a polynomial that can be evaluated by simple substitution:
Lim x->-8 (x-8) = -16.
Therefore
Lim x->-8 (x^2-64)/(x+8) = -16
lim ((x^2-64)/(x+8))
x->-8
1 answer