Question

Evaluate the following limits :

${lim}_{x\to \infty }\frac{(3x-1)(4x-2)}{(x+8)(x-1)}$

Answer 1

${lim}_{x\to \infty }\frac{(3x-1)(4x-2)}{(x+8)(x-1)}$

$\left[Expressionis\frac{\infty }{\infty }\right]$

$={lim}_{x\to \infty }\frac{(12x^2-10x+2)}{(x^2+9x-8)}$

Dividing numerator and denominator by $x^2$

$={lim}_{x\to \infty }\left(\frac{12-\frac{10}{x}+\frac{2}{x^2}}{1+\frac{9}{x}-\frac{8}{x^2}}\right)$

$=\frac{12-0+0}{1+0-1}=12$