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Find the limit of $\frac{\sqrt{2x}+\sqrt{x}+\sqrt{x}}{\sqrt{x\sqrt{x}\sqrt{x}}}$ as $x$ approaches $\infty $

Step-by-step Solution

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Final Answer

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Step-by-step Solution

Problem to solve:

$\lim_{x\to\infty}\left(\frac{\sqrt{2x}+\sqrt{x}+\sqrt{x}}{\sqrt{x\sqrt{x}\sqrt{x}}}\right)$

Specify the solving method

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Combining like terms $\sqrt{x}$ and $\sqrt{x}$

$\lim_{x\to\infty }\left(\frac{\sqrt{2x}+2\sqrt{x}}{\sqrt{x\sqrt{x}\sqrt{x}}}\right)$

Learn how to solve limits to infinity problems step by step online.

$\lim_{x\to\infty }\left(\frac{\sqrt{2x}+2\sqrt{x}}{\sqrt{x\sqrt{x}\sqrt{x}}}\right)$

Unlock the first 3 steps of this solution!

Learn how to solve limits to infinity problems step by step online. Find the limit of ((2x)^1/2+x^1/2x^1/2)/((xx^1/2x^1/2)^1/2) as x approaches \infty. Combining like terms \sqrt{x} and \sqrt{x}. When multiplying exponents with same base we can add the exponents. The power of a product is equal to the product of it's factors raised to the same power. Simplify the fraction \frac{3.414214\sqrt{x}}{x} by x.

Final Answer

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$\lim_{x\to\infty}\left(\frac{\sqrt{2x}+\sqrt{x}+\sqrt{x}}{\sqrt{x\sqrt{x}\sqrt{x}}}\right)$

Main topic:

Limits to Infinity

Related Formulas:

1. See formulas

Time to solve it:

~ 0.04 s