Evaluate the following limit:
lim (x -3) x^2-16x+64/x^3-21x^2+144x-320

Question

Evaluate the following limit: 
lim (x ->3) x^2-16x+64/x^3-21x^2+144x-320

anonymous · Answer

The function is continuous at $x=3$. What do you get when you plug in 3?

anonymous · Answer

i need help with factorising the denominator (the answer is -1/2 by the way)

anonymous · Answer

You don't have to factorise it unless you want to know for sure that it doesn't have a singularity at $x=3$... Before you force yourself to do that, why not try to plug in $x=3$ first?

anonymous · Answer

If you happen to get 0 in the denominator, then you can focus your efforts into factorising it.

anonymous · Answer

alright i got the answer, so I just substitute 3 into the whole question. Does that mean that for every question, we sub the limit in unless when it equals to zero then we factorise it?

anonymous · Answer

That could be your general strategy, sure. What I meant to say is that before you even go about factorising, check to see if there is a discontinuity at the approaching value. If you do get a zero in the denominator, THEN try to factorise the numerator and denominator.

anonymous · Answer

Okay, that is more clear now. Thank you for your help.