Question

а)lim x→3 x^2-x-6/x-3 б)lim→∞ x^3-x^2/x^4-x

Answer 1

$1) lim_{x to 3} frac{(x-3)(x+2)}{x-3}=lim_{x to 3}x+2=5$

$2)lim_{x to infty} frac{x^3-x^2}{x^4-x}=lim_{x to infty} frac{x(x-1)}{(x-1)(x^2+x+1)}=lim_{x to infty} frac{x}{x^2+x+1}= \ =lim_{x to infty} frac{ frac{1}{x}}{1+ frac{1}{x}+ frac{1}{x^2} }= 0$