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Apply the formula: $a^3+b$$=\left(a-\sqrt[3]{\left|b\right|}\right)\left(a^2+a\sqrt[3]{\left|b\right|}+\sqrt[3]{\left|b\right|^{2}}\right)$, where $a=x$ and $b=-1$
Impara online a risolvere i problemi di limiti per sostituzione diretta passo dopo passo.
$\lim_{x\to1}\left(\frac{x^5-1}{\left(x-1\right)\left(x^2+x+1\right)}\right)$
Impara online a risolvere i problemi di limiti per sostituzione diretta passo dopo passo. (x)->(1)lim((x^5-1)/(x^3-1)). Apply the formula: a^3+b=\left(a-\sqrt[3]{\left|b\right|}\right)\left(a^2+a\sqrt[3]{\left|b\right|}+\sqrt[3]{\left|b\right|^{2}}\right), where a=x and b=-1. We can factor the polynomial x^5-1 using the rational root theorem, which guarantees that for a polynomial of the form a_nx^n+a_{n-1}x^{n-1}+\dots+a_0 there is a rational root of the form \pm\frac{p}{q}, where p belongs to the divisors of the constant term a_0, and q belongs to the divisors of the leading coefficient a_n. List all divisors p of the constant term a_0, which equals -1. Next, list all divisors of the leading coefficient a_n, which equals 1. The possible roots \pm\frac{p}{q} of the polynomial x^5-1 will then be.
