Lim_x → 3x^4 81/x^2 9 It is fo the form 0/0 =lim_x → 3(x^2 9)(x^2+9)/(x^2 9)=lim_x → 3 x^2 +9 =(3)^2 +9=9+9=18 ...

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Factorization Method Form to Remove Indeterminate Form

lim x → 3x4-8...

Question

${lim}_{x \to 3} \frac{x^{4} - 81}{x^{2} - 9}$

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Solution

${lim}_{x \to 3} \frac{x^{4} - 81}{x^{2} - 9}$

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

$= {lim}_{x \to 3} \frac{(x^{2} - 9) (x^{2} + 9)}{(x^{2} - 9)} = {lim}_{x \to 3} x^{2} + 9$

$= (3)^{2} + 9 = 9 + 9 = 18$

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