lim _ x→√( 3 ) #160; x ^ 2 3 x ^ 2 3√( 3 ) x 12 #160; #160; #160; #160; #160; #160; #160; #160; #160; [ 00 form ] Appl ...

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Byju's Answer

Standard XII

Mathematics

Algebra of Limits

Evaluate :

Question

Evaluate :

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Solution

${lim}_{x \to \sqrt{3}} \frac{x^{2} - 3}{x^{2} - 3 \sqrt{3} x - 12}$ $[\frac{0}{0} f o r m]$

Applying L'Hospital rule,
$= [\frac{2 x}{2 x + 3 \sqrt{3}}]$ $(w h e r e x = \sqrt{3})$
$= \frac{2 \sqrt{3}}{2 \sqrt{3} + 3 \sqrt{3}}$
$= \frac{2 \sqrt{3}}{5 \sqrt{3}}$
$= \frac{2}{5}$
Hence, the answer is $\frac{2}{5} .$

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Q. Evaluate

\int x^{3} l n x d x

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Evaluate :

limx→√3x2−3x2−3√3x−12 [00form]Applying L'Hospital rule, =[2x2x+3√3] (wherex=√3)=2√32√3+3√3=2√35√3=25Hence, the answer is 25.