If limx - a2x-x2-3a2-x-a-2a- -2 where a- R- then a is equal to

The correct option is D 19 lim _ x→ a 2x √( x ^ 2 +3a^ 2 ) #160; √( x+a ) √( 2a ) #160; #160; #160; Using LHR. ⇒lim _ x→ a 2 (2x) ...

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Multiplication of Surds

If limx → a...

Question

If $lim x \to a \frac{2 x - \sqrt{x^{2} + 3 a^{2}}}{\sqrt{x + a} - \sqrt{2 a}} = \sqrt{2}$ ( where $a \in R^{+}$ ), then $a$ is equal to

\frac{1}{9}

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\frac{1}{2 \sqrt{2}}

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\frac{1}{3 \sqrt{2}}

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None of these

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Solution

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{lim}_{x \to a} \frac{2 x - \sqrt{x^{2} + 3 a^{2}}}{\sqrt{x + a} - \sqrt{2 a}} = \sqrt{2}

a ϵ R^{+}),

l i m x \to a \frac{2 x - \sqrt{x^{2} + {3 a}^{2}}}{\sqrt{x + a} - \sqrt{2 a}} = \sqrt{2}

a \in R^{+})

A^{3} + 2 A^{2} + 5 A + I = 0, then A^{- 1}

- (3 A^{2} + 2 A + 5)

3 A^{2} + 2 A + 5

3 A^{2} - 2 A - 5

A = (\begin{matrix} 3 & 1 - 9 & - 3 \end{matrix})

{(1 + 2 A + 3 A^{2} + . . . . \infty)}^{- 1}

f (x)

4

x = 1

x = 2

lim x \to 0 (\frac{f (x)}{x^{2}} + 1) = 3

f (- 1)

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