Step-by-step Solution

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

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Step-by-step Solution

Problem to solve:

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

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

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

Unlock this full step-by-step solution!

Learn how to solve limits to infinity problems step by step online. Find the limit (x)->(\infty)lim(((2x)^0.5+x^0.5+x^0.5)/((xx^0.5*x^0.5)^0.5)). When multiplying exponents with same base we can add the exponents. When multiplying two powers that have the same base (x), you can add the exponents. The power of a product is equal to the product of it's factors raised to the same power. The square root of 2 is \frac{2}{\sqrt{2}}.

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

Time to solve it:

~ 0.04 s