Find Limit as x approaches 4.

Question

x approaches 4.

x²+2x-24/x²-8x+16

I have factored it down (x+6)(x-4)/(x-4)(x-4), but that leaves me with 10/0 which does not work.

Any help? Thanks

Answer 1

Yes, factoring does work...you just missed the correct conclusion.

Factoring takes out a factor of x-4 from numerator and denominator, but it leaves a bounded expression in the numerator and an unbounded expression in the denominator. This means the whole expression is unbounded near x=4, i.e. no limit exists.