Question

Find the limit. use l'hospital's rule if appropriate. if there is a more elementary method, consider using it. lim x→4 x2 − 16 x2 − 4x

Answer 1

Probably you are supposed to compute

$\displaystyle\lim_{x\to4}\frac{x^2-16}{x^2-4x}$

Factorize the numerator and denominator, then simplify:

$\displaystyle\lim_{x\to4}\frac{(x-4)(x+4)}{x(x-4)}=\lim_{x\to4}\frac{x+4}x=\frac{4+4}4=2$