Question

Lim x tends to 2 x3 -6x2+11x-6/x2-6x+8

Answer 1

$\frac{1}{2}$

Step-by-step explanation:

$Given, \: \: \: lim \: {x}_{\to}2 \: \: \: (\frac{ {x}^{3} - 6 {x}^{2} + 11x - 6 }{ {x}^{2} - 6x + 8 }) \\ use \: \: L' Hospital \: \: rules \\ lim \: {x}_{\to}2 \: \: \: (\frac{ 3{x}^{2} - 12x + 11}{ 2x - 6 }) \\ = \frac{3 \times {2}^{2} - 12 \times 2 + 11 }{2 \times 2 - 6} \\ = \frac{12 - 24 + 11}{4 - 6} \\ = \frac{ - 1}{ - 2} = \frac{1}{2}$