The value of lim x - 2 - 2-43 x-2-x-2 is

Limx→2 nbsp;x2 43x 2 x+2=limx→2 nbsp;x2 43x 2 x+2×3x 2+x+23x 2+x+2=limx→2 nbsp;x2 43x 2+x+23x 22 x+22 nbsp; nbsp;00 nbsp;form=limx→2 nbsp;x 2x+23x ...

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

Byju's Answer

Standard XII

Mathematics

Factorization

The value of ...

Question

The value of $lim x \to 2 \frac{x^{2} - 4}{\sqrt{3 x - 2} - \sqrt{x + 2}}$ is

Open in App

Solution

$lim x \to 2 \frac{x^{2} - 4}{\sqrt{3 x - 2} - \sqrt{x + 2}} = lim x \to 2 \frac{x^{2} - 4}{\sqrt{3 x - 2} - \sqrt{x + 2}} \times \frac{\sqrt{3 x - 2} + \sqrt{x + 2}}{\sqrt{3 x - 2} + \sqrt{x + 2}} = lim x \to 2 \frac{(x^{2} - 4) (\sqrt{3 x - 2} + \sqrt{x + 2})}{{(\sqrt{3 x - 2})}^{2} - {(\sqrt{x + 2})}^{2}} (\frac{0}{0} f o r m) = lim x \to 2 \frac{(x - 2) (x + 2) (\sqrt{3 x - 2} + \sqrt{x + 2})}{3 x - 2 - x - 2} (\frac{0}{0} f o r m) = lim x \to 2 \frac{(x - 2) (x + 2) (\sqrt{3 x - 2} + \sqrt{x + 2})}{2 x - 4} (\frac{0}{0} f o r m) = lim x \to 2 \frac{(x - 2) (x + 2) (\sqrt{3 x - 2} + \sqrt{x + 2})}{2 (x - 2)} (\frac{0}{0} f o r m) = lim x \to 2 \frac{(x + 2) (\sqrt{3 x - 2} + \sqrt{x + 2})}{2} = \frac{(2 + 2) (\sqrt{3 \times 2 - 2} + \sqrt{2 + 2})}{2} = 8$

Suggest Corrections

Similar questions

Q. Find the value of x for which

{(\frac{3}{4})}^{6} \times {(\frac{16}{9})}^{5} = {(\frac{4}{3})}^{x + 2}

Q. The value of

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

Q. The value of

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

Write the value of ${lim}_{x \to 2} \frac{| x - 2 |}{x - 2} .$

The value of ${lim}_{x \to \infty} x [t a n^{- 1} (\frac{x + 2}{x + 2}) - t a n^{- 1} (\frac{x}{x + 2})] i s$

Join BYJU'S Learning Program

The value of limx→2 x2−4√3x−2−√x+2 is

The value of $lim x \to 2 \frac{x^{2} - 4}{\sqrt{3 x - 2} - \sqrt{x + 2}}$ is