Lim x - 5x-5-6 x-5-4 x-5

Lim_x → 5x 5/√(6x 5) √(4x+5) Rationalising the denominator =lim_x → 5x 5/(√(6x 5) √(4x+5))×(√(6x 5)+√(4x+5))/(√(6x 5)+√(4x+5)) =lim_x → 5(x 5)(√(6x 5)+√(4x+5))/ ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Rationalization Method to Remove Indeterminate Form

lim x → 5x-5/...

Question

${lim}_{x \to 5} \frac{x - 5}{\sqrt{6 x - 5} - \sqrt{4 x + 5}}$

Open in App

Solution

${lim}_{x \to 5} \frac{x - 5}{\sqrt{6 x - 5} - \sqrt{4 x + 5}}$

Rationalising the denominator

$= {lim}_{x \to 5} \frac{x - 5}{(\sqrt{6 x - 5} - \sqrt{4 x + 5})} \times \frac{(\sqrt{6 x - 5} + \sqrt{4 x + 5})}{(\sqrt{6 x - 5} + \sqrt{4 x + 5})}$

$= {lim}_{x \to 5} \frac{(x - 5) (\sqrt{6 x - 5} + \sqrt{4 x + 5})}{(6 x - 5) - (4 x + 5)}$

$= {lim}_{x \to 5} \frac{(x - 5) (\sqrt{6 x - 5} + \sqrt{4 x + 5})}{2 x - 10}$

$= {lim}_{x \to 5} \frac{(x - 5) (\sqrt{6 x - 5} + \sqrt{4 x + 5})}{2 (x - 5)}$

$= \frac{\sqrt{6 (5) - 5} + \sqrt{4 (5) + 5}}{2}$

$= \frac{\sqrt{25} + \sqrt{25}}{2}$

$= \frac{5 + 5}{2} = 5$

Suggest Corrections

Similar questions

Q. Solve

lim x \to 5 \frac{x - 5}{\sqrt{6 x - 5} - \sqrt{4 x + 5}}

Q. Solve:

lim x \to 5 \frac{x - 5}{\sqrt{6 x - 5} - \sqrt{4 x + 5}}

\lim_{x \to 5} \frac{x - 5}{\sqrt{6 x - 5} - \sqrt{4 x + 5}}

Q. Evaluate the limit to infinity

lim x \to \infty \frac{{3 x}^{- 1} + {4 x}^{- 2}}{{5 x}^{- 1} + 6 x^{- 2}} = \frac{3}{5}

l i m_{x \to \infty} \frac{\sqrt{4 x^{2} + 5 x + 8}}{4 x + 5}

is equal to

Join BYJU'S Learning Program

limx→5x−5√6x−5−√4x+5

${lim}_{x \to 5} \frac{x - 5}{\sqrt{6 x - 5} - \sqrt{4 x + 5}}$