Lim_x → 2x^3 8/x^2 4 It is of the form form 0/0 =lim_x → 2(x 2)(x^2+4+2x)/(x 2)(x+2) =lim_x → 2x^2+2x+4/x+2 =(2)^2+4+2(2)/2+2=4+4+4/4=12/4=3 ...

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Limit

lim x → 2x3-8...

Question

${lim}_{x \to 2} \frac{x^{3} - 8}{x^{2} - 4}$

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Solution

${lim}_{x \to 2} \frac{x^{3} - 8}{x^{2} - 4}$

It is of the form form $\frac{0}{0}$

$= {lim}_{x \to 2} \frac{(x - 2) (x^{2} + 4 + 2 x)}{(x - 2) (x + 2)}$

$= {lim}_{x \to 2} \frac{x^{2} + 2 x + 4}{x + 2}$

$= \frac{(2)^{2} + 4 + 2 (2)}{2 + 2} = \frac{4 + 4 + 4}{4} = \frac{12}{4} = 3$

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