Find the limits of the following rational functions, aware that if the limit of the denominator equals zero, neither Rule 6 nor the generalized rule for rational functions used above apply.

The limit of the denominator is zero, so Rule 6 cannot be used. Since we are only interested in the function as x draws near to 9, however, the limit can be found if by factoring and canceling, the problem of zero in the denominator is resolved.

With the limit of the denominator still equal to zero and no possibility of further factoring, the limit does not exist.

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6-x (a) lim- x-9x2-81