Lim x - 1-5 x-4-x-x2-1

Lim_x → 1√(5x 4) √(x)/x^2 1 Rationalising the numenator =lim_x → 1(√(5x 4) √(x))/(x 1)(x+1)×(√(5x 4)+√(x))/(√(5x 4)+√(x)) =lim_x → 1((5 4) x)/(x 1)(x+1)(√(5x 4) ...

You visited us 3 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Rationalization Method to Remove Indeterminate Form

lim x → 1√5 x...

Question

${lim}_{x \to 1} \frac{\sqrt{5 x - 4} - \sqrt{x}}{x^{2} - 1}$

Open in App

Solution

${lim}_{x \to 1} \frac{\sqrt{5 x - 4} - \sqrt{x}}{x^{2} - 1}$

Rationalising the numenator

$= {lim}_{x \to 1} \frac{(\sqrt{5 x - 4} - \sqrt{x})}{(x - 1) (x + 1)} \times \frac{(\sqrt{5 x - 4} + \sqrt{x})}{(\sqrt{5 x - 4} + \sqrt{x})}$

$= {lim}_{x \to 1} \frac{((5 - 4) - x)}{(x - 1) (x + 1) (\sqrt{5 x - 4} + \sqrt{x})}$

$= {lim}_{x \to 1} \frac{4 (x - 1)}{(x - 1) (x + 1) (\sqrt{5 x - 4} + \sqrt{x})}$

$= {lim}_{x \to 1} \frac{4}{(x + 1) (\sqrt{5 x - 4} + \sqrt{x})}$

$= \frac{4}{(1 + 1) (\sqrt{5 - 4} + \sqrt{1})}$

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

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

Suggest Corrections

Similar questions

Q. Find the limits :

i .

lim x \to 1 [\frac{x^{2} + 1}{x + 100}]

i i .

lim x \to 2 [\frac{x^{3} - 4 x^{2} + 4 x}{x^{2} - 4}]

i i i .

lim x \to 2 [\frac{x^{2} - 4}{x^{3} - 4 x^{2} + 4 x}]

i v .

lim x \to 2 [\frac{x^{3} - 2 x^{2}}{x^{2} - 5 x + 6}]

v .

lim x \to 1 [\frac{x - 2}{x^{2} - x} - \frac{1}{x^{3} - 3 x^{2} + 2 x}]

Q. Assertion(A):

lim x \to \infty {(\frac{x^{2} + 5 x + 3}{x^{2} + x + 2})}^{x} = e^{4}

Reason(R):

lim x \to \infty (1 + x)^{1 / x} = e

lim x \to \infty \frac{7 x^{2} - 5 x + 6}{x^{2} + x + 1}

= ______

${lim}_{x \to 1} \frac{\sqrt{5 x - 4} - \sqrt{x}}{x - 1}$

${lim}_{x \to 1} \frac{\sqrt{5 x - 4} - - \sqrt{x}}{x^{3} - 1}$

Join BYJU'S Learning Program

limx→1√5x−4−√xx2−1

limx→1√5x−4−√xx2−1 Rationalising the numenator =limx→1(√5x−4−√x)(x−1)(x+1)×(√5x−4+√x)(√5x−4+√x) =limx→1((5−4)−x)(x−1)(x+1)(√5x−4+√x) =limx→14(x−1)(x−1)(x+1)(√5x−4+√x) =limx→14(x+1)(√5x−4+√x) =4(1+1)(√5−4+√1) =42(1+1) =44=1

${lim}_{x \to 1} \frac{\sqrt{5 x - 4} - \sqrt{x}}{x^{2} - 1}$