Lim_x → 2x^4 16/(x 2) =lim_x → 2(x^2 4)(x^2+4)/(x 2) =lim_x → 2(x 2)(x+2)(x^2+4)/(x 2) =lim_x → 2(x+2)(x^2+4) =(2+2)(4+4) =4(8)=32 ...

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Factorization Method Form to Remove Indeterminate Form

lim x → 2x4-1...

Question

${lim}_{x \to 2} \frac{x^{4} - 16}{x - 2}$

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Solution

${lim}_{x \to 2} \frac{x^{4} - 16}{(x - 2)}$

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

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

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

=(2+2)(4+4)

=4(8)=32

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