Lim x- x 2 - a 2 - x 2 - a 2 -

The correct option is C 0 lim _ x→∞ #160;{√( x ^ 2 + a ^ 2 ) √( x ^ 2 a ^ 2)} =lim _ x→∞ #160; (√( x ^ 2 + a ^ 2 ) √( x ^ 2 a ^ 2 ) )√ ...

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Theorems for Differentiability

lim x→∞√ x 2 ...

Question

${lim}_{x \to \infty} {\sqrt{x^{2} + a^{2}} - \sqrt{x^{2} - a^{2}}} =$

a^{2}

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2 a^{2}

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0

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- a^{2}

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$lim x \to \infty (\sqrt{x^{2} + a x + a^{2}} - \sqrt{x^{2} + a^{2}}) =$

y = \frac{\sqrt{(a^{2} + x^{2})} + \sqrt{(a^{2} - x^{2})}}{\sqrt{(a^{2} + x^{2})} - \sqrt{(a^{2} - x^{2})}}

\frac{d y}{d x} = - \frac{2 a^{2}}{x^{3}} {1 + \frac{a^{2}}{\sqrt{(a^{4} - x^{4})}}}

{lim}_{x \to \infty} (\sqrt{x^{2} + a x + a^{2}} - \sqrt{x^{2} + a^{2}})

The value of ${lim}_{x \to 0} \frac{\sqrt{a^{2} - a x + x^{2}} - \sqrt{a^{2} + a x + x^{2}}}{\sqrt{a + x} - \sqrt{a - x}}$ is

x = \frac{\sqrt{a^{2} + b^{2}} + \sqrt{a^{2} - b^{2}}}{\sqrt{a^{2} + b^{2}} - \sqrt{a^{2} - b^{2}}}

a^{2} - b^{2} = \frac{2 a^{2}}{x^{2} + 1}

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