Lim_x → 42 √(x)/4 x Rationalising the numerator =lim_x → 4(2 √(x))(2+√(x))/(4 x)(2+√(x)) =lim_x → 4(2)^2 (√(x))^2/(4 x)(2+√(x)) =lim_x → 4(4 x)/(4 x)(2+√(x)) =1 ...

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Byju's Answer

Standard XII

Mathematics

Rationalization Method to Remove Indeterminate Form

lim x → 42-√x...

Question

${lim}_{x \to 4} \frac{2 - \sqrt{x}}{4 - x}$

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Solution

${lim}_{x \to 4} \frac{2 - \sqrt{x}}{4 - x}$

Rationalising the numerator

$= {lim}_{x \to 4} \frac{(2 - \sqrt{x}) (2 + \sqrt{x})}{(4 - x) (2 + \sqrt{x})}$

$= {lim}_{x \to 4} \frac{(2)^{2} - (\sqrt{x})^{2}}{(4 - x) (2 + \sqrt{x})}$

$= {lim}_{x \to 4} \frac{(4 - x)}{(4 - x) (2 + \sqrt{x})}$

$= \frac{1}{2 + \sqrt{4}}$

$= \frac{1}{2 + 2} = \frac{1}{4}$

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Similar questions

\lim_{x \to 4} \frac{2 - \sqrt{x}}{4 - x}

42(4+2) = (42 x 4) + (42 x 2) is an example of:

lim x \to \frac{π}{4}

\int_{2}^{{sec}^{2} x} \frac{f (t) d t}{x^{2} - {\frac{π}{4}}^{2}}

lim x \to - 4 \frac{| x - 4 |}{x - 4}

Q. If

f (x) = [x] - [\frac{x}{4}], x \in R

, where

[x]

denotes the greatest integer function, then :

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limx→42−√x4−x

limx→42−√x4−x Rationalising the numerator =limx→4(2−√x)(2+√x)(4−x)(2+√x) =limx→4(2)2−(√x)2(4−x)(2+√x) =limx→4(4−x)(4−x)(2+√x) =12+√4 =12+2=14

${lim}_{x \to 4} \frac{2 - \sqrt{x}}{4 - x}$