can someone please show me how to solve
lim x->2 $\displaystyle \frac{x^2-4x+4}{x^3-3x^2+4}$?
i think u have to use L'Hopitals, but im not sure. and im not clear on L'Hops, either
Yes you can use l'hospitals.
OR you can see that x = 2 is a root/divisor of both polynomials,
so factoring would break this limit.
L'hopitals Rule is easier because all you have to do it differentiate the top and bottom polynomial twice.
You arrive at the expression
$\displaystyle \frac{2}{6x-6} = \frac{1}{3}$ as x-->2