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Operations with infinity Calculator

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1

Solved example of Operations with infinity

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

When multiplying exponents with same base we can add the exponents

$\lim_{x\to\infty}\left(\frac{\sqrt{2x}+\sqrt{x}+\sqrt{x}}{\sqrt{x\cdot x}}\right)$
3

When multiplying exponents with same base you can add the exponents

$\lim_{x\to\infty}\left(\frac{\sqrt{2x}+\sqrt{x}+\sqrt{x}}{\sqrt{x^2}}\right)$
4

The power of a product is equal to the product of it's factors raised to the same power

$\lim_{x\to\infty}\left(\frac{\sqrt{2}\sqrt{x}+\sqrt{x}+\sqrt{x}}{\sqrt{x^2}}\right)$
5

Adding $\sqrt{2}\sqrt{x}$ and $\sqrt{x}$

$\lim_{x\to\infty}\left(\frac{\sqrt{x}+\sqrt[3]{33}\sqrt{x}}{\sqrt{x^2}}\right)$
6

Applying the power of a power property

$\lim_{x\to\infty}\left(\frac{\sqrt{x}+\sqrt[3]{33}\sqrt{x}}{x}\right)$
7

Adding $\sqrt[3]{33}\sqrt{x}$ and $\sqrt{x}$

$\lim_{x\to\infty}\left(\frac{3.4142\sqrt{x}}{x}\right)$
8

Simplifying the fraction by $x$

$\lim_{x\to\infty}\left(3.4142x^{-\frac{1}{2}}\right)$
9

Evaluating the limit when $x$ tends to $\infty$

$3.4142\infty^{-\frac{1}{2}}$
10

Simplifying

$3.4142\infty^{-\frac{1}{2}}$
11

Infinity to the power of any negative number is equal to $0$

$0$

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