Limx-2-x-3-x-5-x-3x-2-2x-3-

The correct option is A 2/√(3) lim _ x→∞ #160; 2√( x ) +3√( x ) +5√( x ) #160; √( 3x 2 ) +√( 2x 3 ) #160; #160; =lim _ x→∞ #160; √( ...

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Standard XII

Mathematics

Algebra of Derivatives

limx→∞2√x+3√x...

Question

$lim x \to \infty \frac{2 \sqrt{x} + 3 \sqrt[3]{x} + 5 \sqrt[5]{x}}{\sqrt{3 x - 2} + \sqrt[3]{2 x - 3}} =$

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

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\sqrt{3}

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

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

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Solution

The correct option is A $\frac{2}{\sqrt{3}}$
$lim x \to \infty \frac{2 \sqrt{x} + 3 \sqrt[3]{x} + 5 \sqrt[5]{x}}{\sqrt{3 x - 2} + \sqrt[3]{2 x - 3}}$

$= lim x \to \infty \frac{\sqrt{x} (2 + \frac{3}{\sqrt[6]{x}} + \frac{5}{x^{3 / 10}})}{\sqrt{x} (\sqrt{3 - \frac{2}{x}} + \sqrt[3]{\frac{2}{x^{1 / 2}} - \frac{3}{x^{3 / 2}}})}$

$= \frac{2 + 0 + 0}{\sqrt{3 - 0} + \sqrt[3]{0 - 0}} = \frac{2}{\sqrt{3}} [x \to \infty, \frac{1}{x^{n}} \to 0, n > 0]$

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limx→∞2√x+33√x+55√x√3x−2+3√2x−3=

The correct option is A 2√3limx→∞2√x+33√x+55√x√3x−2+3√2x−3=limx→∞√x(2+36√x+5x3/10)√x(√3−2x+3√2x1/2−3x3/2)=2+0+0√3−0+3√0−0=2√3[x→∞,1xn→0,n>0]

$lim x \to \infty \frac{2 \sqrt{x} + 3 \sqrt[3]{x} + 5 \sqrt[5]{x}}{\sqrt{3 x - 2} + \sqrt[3]{2 x - 3}} =$