Lim_x → 2√(3 x) 1/2 x Rationalising the numerator =lim_x → 2(√(3 x) 1)/2 x×(√(3 x)+1)/(√(3 x)+1) =lim_x → 2(3 x) 1/(2 x)(√(3 x)+1) =lim_x → 2(2 x)/(2 x)(√(3 x) ...

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Byju's Answer

Standard XII

Mathematics

Rationalization Method to Remove Indeterminate Form

lim x → 2√3-x...

Question

${lim}_{x \to 2} \frac{\sqrt{3 - x} - 1}{2 - x}$

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Solution

${lim}_{x \to 2} \frac{\sqrt{3 - x} - 1}{2 - x}$

Rationalising the numerator

$= {lim}_{x \to 2} \frac{(\sqrt{3 - x} - 1)}{2 - x} \times \frac{(\sqrt{3 - x} + 1)}{(\sqrt{3 - x} + 1)}$

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

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

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

$= \frac{1}{\sqrt{3 - 2} + 1} = \frac{1}{1 + 1} = \frac{1}{2}$

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Similar questions

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$(i i) {lim}_{x \to 2^{-}} \frac{x - 3}{x^{2} - 4}$

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$(v i) {lim}_{x \to \frac{π^{-}}{2}} t a n x$

$(v i i) {lim}_{x \to \frac{π}{2^{+}}} s e c x$

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Q. Solve :

lim x \to 2 \frac{\sqrt{1 +} \sqrt{2 + x} - \sqrt{3}}{x - 2}

Q. Evaluate:

lim x \to 2 \frac{\sqrt{3 - x} - 1}{2 - x}

{lim}_{x \to 1} \frac{1 - x^{- 1 / 3}}{1 - x^{- 2 / 3}}

Q. Evaluate:

{lim}_{x \to 1} \frac{1 - x^{\frac{- 1}{3}}}{1 - x^{\frac{- 2}{3}}}

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limx→2√3−x−12−x

limx→2√3−x−12−x Rationalising the numerator =limx→2(√3−x−1)2−x×(√3−x+1)(√3−x+1) =limx→2(3−x)−1(2−x)(√3−x+1) =limx→2(2−x)(2−x)(√3−x+1) =limx→21(√3−x+1) =1√3−2+1=11+1=12

${lim}_{x \to 2} \frac{\sqrt{3 - x} - 1}{2 - x}$