Question

Determina el valor del siguiente limite de funciones racionales

Answer 1

$\lim_{x \to 1} \frac{ x^{9}+2 x^{2}-x-2 }{ x^{2} +3x-4}$
$= \lim_{x \to 1} \frac{(x-1)( x^{8} + x^{7}+ x^{6} + x^{5}+ x^{4}+ x^{3}+ x^{2}+3x+2) }{(x-1)(x+4)}$
$= \lim_{x \to 1} \frac{ x^{8} + x^{7}+ x^{6} + x^{5}+ x^{4}+ x^{3}+ x^{2}+3x+2 }{x+4}= \frac{1+1+1+1+1+1+1+3+2}{1+4}$
$=\frac{12}{5}$

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