Question

lim(x^3-4x^2-5x)/(25-x^2)

x-->5

Answer 1

$<var>\\\lim_{x\to5}\frac{x^3-4x^2-5x}{25-x^2}=\\ \lim_{x\to5}\frac{x(x^2-4x-5}{(x-5)(x+5)}=\\ \lim_{x\to5}\frac{x(x^2+x-5x-5)}{(x-5)(x+5)}=\\ \lim_{x\to5}\frac{x(x(x+1)-5(x+1))}{(x-5)(x+5)}=\\ \lim_{x\to5}\frac{x(x-5)(x+1)}{(x-5)(x+5)}=\\ \lim_{x\to5}\frac{x(x+1)}{x+5}=\\ \frac{5(5+1)}{5+5}=\\ \frac{5\cdot6}{10}=\\ \frac{6}{2}=\\ 3 </var>$