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

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Expansions to Remove Indeterminate Form

lim x → 4x2-1...

Question

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

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Solution

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

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

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

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

=(2+2)(4+4)

=4(8) =32

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