Find b x- 2alim- x-2a -x-2a- x2-4a2 is 1b-a

x→ 2alim√( ( x 2a ))+√(x) √(2a)/√( ( x^2 4a^2 )) Split into two terms and rationalize. x→ 2alim1/√( ( x+2a ))+x→ 2alimx 2a/√(x+√( ( 2a ))).√( ( x^2 ...

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Byju's Answer

Standard XII

Mathematics

Formation of a Differential Equation from a General Solution

Find b x→ 2...

Question

Find b $l i m x \to 2 a \frac{\sqrt{(x - 2 a)} + \sqrt{x} - \sqrt{2 a}}{\sqrt{(x^{2} - 4 a^{2})}}$ is $\frac{1}{b \sqrt{a}}$

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Solution

$l i m x \to 2 a \frac{\sqrt{(x - 2 a)} + \sqrt{x} - \sqrt{2 a}}{\sqrt{(x^{2} - 4 a^{2})}}$
Split into two terms and rationalize.
$l i m x \to 2 a \frac{1}{\sqrt{(x + 2 a)}} + l i m x \to 2 a \frac{x - 2 a}{\sqrt{x + \sqrt{(2 a)}}} . \frac{\sqrt{(x^{2} - 4 a^{2})}}{(x^{2} - 4 a^{2})}$
$= \frac{1}{2 \sqrt{a}} + l i m x \to 2 a \frac{1}{\sqrt{x +} \sqrt{(2 a)}} . \frac{\sqrt{(x^{2} - 4 a^{2})}}{x + 2 a} = \frac{1}{2 \sqrt{a}} + 0$

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Find b limx→2a√(x−2a)+√x−√2a√(x2−4a2) is 1b√a

limx→2a√(x−2a)+√x−√2a√(x2−4a2)Split into two terms and rationalize. limx→2a1√(x+2a)+limx→2ax−2a√x+√(2a).√(x2−4a2)(x2−4a2)=12√a+limx→2a1√x+√(2a).√(x2−4a2)x+2a=12√a+0

Find b $l i m x \to 2 a \frac{\sqrt{(x - 2 a)} + \sqrt{x} - \sqrt{2 a}}{\sqrt{(x^{2} - 4 a^{2})}}$ is $\frac{1}{b \sqrt{a}}$