X - 2lim3x - 33-x-123-x-2-31-x is equal to

X → 2lim3^x + 273^x 1213^x/2 33^x Put 3^x/2 = t t → 3limt^2 + 27t^2 12 nbsp; 1t 3t^2 = t → 3lim(t^2 9)(t^2 3)(t 3) = t → 3lim (t^2 3) (t + 3) = 36 ...

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Byju's Answer

Standard XI

Mathematics

L'Hospital Rule to Remove Indeterminate Form

x → 2lim3x + ...

Question

$lim x \to 2 \frac{3^{x} + 3^{3 - x} - 12}{3^{\frac{- x}{2}} - 3^{1 - x}}$ is equal to

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Solution

$lim x \to 2 \frac{3^{x} + \frac{27}{3^{x}} - 12}{\frac{1}{3^{x / 2}} - \frac{3}{3^{x}}}$

Put $3^{x / 2} = t$
$lim t \to 3 \frac{t^{2} + \frac{27}{t^{2}} - 12}{\frac{1}{t} - \frac{3}{t^{2}}}$

$= lim t \to 3 \frac{(t^{2} - 9) (t^{2} - 3)}{(t - 3)} = lim t \to 3 (t^{2} - 3) (t + 3) = 36$

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limx→23x+33−x−123−x2−31−x is equal to

limx→23x+273x−1213x/2−33x Put 3x/2=t limt→3t2+27t2−121t−3t2 =limt→3(t2−9)(t2−3)(t−3)=limt→3(t2−3)(t+3)=36

$lim x \to 2 \frac{3^{x} + 3^{3 - x} - 12}{3^{\frac{- x}{2}} - 3^{1 - x}}$ is equal to

$lim x \to 2 \frac{3^{x} + \frac{27}{3^{x}} - 12}{\frac{1}{3^{x / 2}} - \frac{3}{3^{x}}}$

Put $3^{x / 2} = t$
$lim t \to 3 \frac{t^{2} + \frac{27}{t^{2}} - 12}{\frac{1}{t} - \frac{3}{t^{2}}}$

$= lim t \to 3 \frac{(t^{2} - 9) (t^{2} - 3)}{(t - 3)} = lim t \to 3 (t^{2} - 3) (t + 3) = 36$