mathop {lim }limits_{x to a} frac{{sqrt {a + | vedclass

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Question

(A) આપેલ લક્ષ: $L = \mathop {\lim }\limits_{x 	o a} \frac{{\sqrt {a + 2x} - \sqrt {3x} }}{{\sqrt {3a + x} - 2\sqrt x }}$અંશ અને છેદનું સંમેયીકરણ કરતા

Vedclass · Accepted Answer

$\frac{1}{{\sqrt 3 }}$

Vedclass · Answer

(A) આપેલ લક્ષ: $L = \mathop {\lim }\limits_{x 	o a} \frac{{\sqrt {a + 2x} - \sqrt {3x} }}{{\sqrt {3a + x} - 2\sqrt x }}$અંશ અને છેદનું સંમેયીકરણ કરતા:$L = \mathop {\lim }\limits_{x 	o a} \frac{a - x}{3(a - x)} 	imes \frac{\sqrt {3a + x} + 2\sqrt x}{\sqrt {a + 2x} + \sqrt {3x}}$$L = \frac{1}{3} 	imes \frac{2\sqrt{4a} + 2\sqrt{a}}{2\sqrt{3a}} = \frac{1}{\sqrt{3}}$.

$\mathop {\lim }\limits_{x \to a} \frac{{\sqrt {a + 2x} - \sqrt {3x} }}{{\sqrt {3a + x} - 2\sqrt x }} = \dots$ (જ્યાં $a \ne 0$)

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