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Limits by factoring Calculator

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1

Solved example of limits by factoring

$\lim_{x\to∞}\left(\frac{x^3+1}{3x^3-1}\right)$
2

Factor the sum of cubes: $a^3+b^3 = (a+b)(a^2-ab+b^2)$

$\lim_{x\to∞}\left(\frac{\left(x+\sqrt[3]{1}\right)\left(x^2-1\left(\sqrt[3]{1}\right)x+\sqrt[3]{\left(1\right)^{2}}\right)}{3x^3-1}\right)$
3

Calculate the power $\sqrt[3]{\left(1\right)^{2}}$

$\lim_{x\to∞}\left(\frac{\left(x+1\right)\left(x^2-11x+1\right)}{3x^3-1}\right)$
4

Apply the formula: $-x$, where $x=1$

$\lim_{x\to∞}\left(\frac{\left(x+1\right)\left(x^2-x+1\right)}{3x^3-1}\right)$
5

Factoring by $x$

$\lim_{x\to∞}\left(\frac{\left(x+1\right)\left(x\left(x^{\left(2-1\right)}-1\right)+1\right)}{3x^3-1}\right)$
6

Subtract the values $2$ and $-1$

$\lim_{x\to∞}\left(\frac{\left(x+1\right)\left(x\left(x^{1}-1\right)+1\right)}{3x^3-1}\right)$
7

Any expression to the power of $1$ is equal to that same expression

$\lim_{x\to∞}\left(\frac{\left(x+1\right)\left(x\left(x-1\right)+1\right)}{3x^3-1}\right)$
8

Evaluating the limit when $x$ tends to $∞$

$\frac{\left(∞+1\right)\left(∞\left(∞-1\right)+1\right)}{3∞^3-1}$

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