Lim x - 3x2-91-x-3-1-x-3

Lim_x → 3(x^2 9) ( 1/x+3+1/x 3 ) =lim_x → 3(x^2 9) [ x 3+x+3/(x+3)(x 3) ] =lim_x → 3(x^2 9) [ 2x/(x+3)(x 3) ] =lim_x → 3(x 3)(x+3)(2x)/(x+3)(x 3) =lim_x → 32(x ...

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Byju's Answer

Standard XII

Mathematics

Factorization Method Form to Remove Indeterminate Form

lim x → 3x2-9...

Question

${lim}_{x \to 3} (x^{2} - 9) (\frac{1}{x + 3} + \frac{1}{x - 3})$

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Solution

${lim}_{x \to 3} (x^{2} - 9) (\frac{1}{x + 3} + \frac{1}{x - 3})$

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

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

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

$= {lim}_{x \to 3} 2 (x) = 2 (3) = 6$

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limx→3(x2−9)(1x+3+1x−3)

limx→3(x2−9)(1x+3+1x−3) =limx→3(x2−9)[x−3+x+3(x+3)(x−3)] =limx→3(x2−9)[2x(x+3)(x−3)] =limx→3(x−3)(x+3)(2x)(x+3)(x−3) =limx→32(x)=2(3)=6

${lim}_{x \to 3} (x^{2} - 9) (\frac{1}{x + 3} + \frac{1}{x - 3})$