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Calcolatrice di Limiti all'infinito

Risolvete i vostri problemi di matematica con la nostra calcolatrice Limiti all'infinito passo-passo. Migliorate le vostre abilità matematiche con il nostro ampio elenco di problemi impegnativi. Trova tutte le nostre calcolatrici qui.

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1

Qui vi mostriamo un esempio di soluzione passo-passo di limiti all'infinito. Questa soluzione è stata generata automaticamente dalla nostra calcolatrice intelligente:

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

Applicare la formula: $\frac{a}{b}$$=\frac{\frac{a}{fgrow\left(b\right)}}{\frac{b}{fgrow\left(b\right)}}$, dove $a=2x^3-2x^2+x-3$, $b=x^3+2x^2-x+1$ e $a/b=\frac{2x^3-2x^2+x-3}{x^3+2x^2-x+1}$

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

Applicare la formula: $\frac{a}{b}$$=\frac{splitfrac\left(a\right)}{splitfrac\left(b\right)}$, dove $a=\frac{2x^3-2x^2+x-3}{x^3}$ e $b=\frac{x^3+2x^2-x+1}{x^3}$

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

Applicare la formula: $\frac{a}{a}$$=1$, dove $a=x^3$ e $a/a=\frac{2x^3}{x^3}$

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

Applicare la formula: $\frac{a}{a}$$=1$, dove $a/a=\frac{-3}{x^3}$

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

Applicare la formula: $\frac{a}{a^n}$$=\frac{1}{a^{\left(n-1\right)}}$, dove $a=x$ e $n=3$

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

Applicare la formula: $\frac{a}{a^n}$$=\frac{1}{a^{\left(n-1\right)}}$, dove $a=x$ e $n=3$

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

Applicare la formula: $\frac{a^m}{a^n}$$=\frac{1}{a^{\left(n-m\right)}}$, dove $a=x$, $m=2$ e $n=3$

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

Applicare la formula: $a+b$$=a+b$, dove $a=3$, $b=-2$ e $a+b=3-2$

$\lim_{x\to \infty }\left(\frac{2+\frac{-2x^2}{x^3}+\frac{1}{x^{2}}+\frac{-3}{x^3}}{1+\frac{2}{x^{1}}+\frac{-1}{x^{2}}+\frac{1}{x^3}}\right)$
7

Applicare la formula: $\frac{a^m}{a^n}$$=\frac{1}{a^{\left(n-m\right)}}$, dove $a=x$, $m=2$ e $n=3$

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

Applicare la formula: $\frac{a^m}{a^n}$$=\frac{1}{a^{\left(n-m\right)}}$, dove $a=x$, $m=2$ e $n=3$

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

Applicare la formula: $a+b$$=a+b$, dove $a=3$, $b=-2$ e $a+b=3-2$

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

Applicare la formula: $\frac{a^m}{a^n}$$=\frac{1}{a^{\left(n-m\right)}}$, dove $a=x$, $m=2$ e $n=3$

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

Applicare la formula: $a+b$$=a+b$, dove $a=3$, $b=-2$ e $a+b=3-2$

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

Applicare la formula: $x^1$$=x$

$\lim_{x\to \infty }\left(\frac{2+\frac{-2}{x^{1}}+\frac{1}{x^{2}}+\frac{-3}{x^3}}{1+\frac{2}{x}+\frac{-1}{x^{2}}+\frac{1}{x^3}}\right)$
8

Applicare la formula: $\frac{a^m}{a^n}$$=\frac{1}{a^{\left(n-m\right)}}$, dove $a=x$, $m=2$ e $n=3$

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

Applicare la formula: $x^1$$=x$

$\lim_{x\to \infty }\left(\frac{2+\frac{-2}{x}+\frac{1}{x^{2}}+\frac{-3}{x^3}}{1+\frac{2}{x}+\frac{-1}{x^{2}}+\frac{1}{x^3}}\right)$
9

Applicare la formula: $x^1$$=x$

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

Valutare il limite $\lim_{x\to \infty }\left(\frac{2+\frac{-2}{x}+\frac{1}{x^{2}}+\frac{-3}{x^3}}{1+\frac{2}{x}+\frac{-1}{x^{2}}+\frac{1}{x^3}}\right)$ sostituendo tutte le occorrenze di $x$ con $\infty $

$\frac{2+\frac{-2}{\infty }+\frac{1}{\infty ^{2}}+\frac{-3}{\infty ^3}}{1+\frac{2}{\infty }+\frac{-1}{\infty ^{2}}+\frac{1}{\infty ^3}}$

Applicare la formula: $\frac{a}{b}$$=0$, dove $a=-2$ e $b=\infty $

$\frac{2+\frac{1}{\infty ^{2}}+\frac{-3}{\infty ^3}}{1+\frac{-1}{\infty ^{2}}+\frac{1}{\infty ^3}}$

Applicare la formula: $\infty ^n$$=\infty $, dove $\infty=\infty $, $\infty^n=\infty ^3$ e $n=3$

$2+\frac{-2}{\infty }+\frac{1}{\infty }+\frac{-3}{\infty }$

Applicare la formula: $\infty ^n$$=\infty $, dove $\infty=\infty $, $\infty^n=\infty ^3$ e $n=3$

$2+\frac{-2}{\infty }+\frac{1}{\infty }+\frac{-3}{\infty }$

Applicare la formula: $\infty ^n$$=\infty $, dove $\infty=\infty $, $\infty^n=\infty ^3$ e $n=3$

$2+\frac{1}{\infty }+\frac{-3}{\infty }$

Applicare la formula: $\infty ^n$$=\infty $, dove $\infty=\infty $, $\infty^n=\infty ^3$ e $n=3$

$2+\frac{1}{\infty }+\frac{-3}{\infty }$

Applicare la formula: $\infty ^n$$=\infty $, dove $\infty=\infty $, $\infty^n=\infty ^3$ e $n=3$

$\frac{2+\frac{1}{\infty ^{2}}+\frac{-3}{\infty ^3}}{1+\frac{-1}{\infty }+\frac{1}{\infty }}$

Applicare la formula: $\infty ^n$$=\infty $, dove $\infty=\infty $, $\infty^n=\infty ^{2}$ e $n=2$

$\frac{2+\frac{1}{\infty }+\frac{-3}{\infty ^3}}{1+\frac{-1}{\infty }+\frac{1}{\infty }}$

Applicare la formula: $\infty ^n$$=\infty $, dove $\infty=\infty $, $\infty^n=\infty ^3$ e $n=3$

$\frac{2+\frac{1}{\infty }+\frac{-3}{\infty }}{1+\frac{-1}{\infty }+\frac{1}{\infty }}$

Applicare la formula: $\frac{a}{b}+\frac{c}{b}$$=\frac{a+c}{b}$, dove $a=-1$, $b=\infty $ e $c=1$

$\frac{2+\frac{1}{\infty }+\frac{-3}{\infty }}{1+\frac{-1+1}{\infty }}$

Applicare la formula: $\frac{a}{b}+\frac{c}{b}$$=\frac{a+c}{b}$, dove $a=1$, $b=\infty $ e $c=-3$

$2+\frac{1-3}{\infty }$

Applicare la formula: $\frac{a}{b}+\frac{c}{b}$$=\frac{a+c}{b}$, dove $a=1$, $b=\infty $ e $c=-3$

$2+\frac{1-3}{\infty }$

Applicare la formula: $\frac{a}{b}+\frac{c}{b}$$=\frac{a+c}{b}$, dove $a=-1$, $b=\infty $ e $c=-3$

$2+\frac{-1-3}{\infty }$

Applicare la formula: $\frac{a}{b}+\frac{c}{b}$$=\frac{a+c}{b}$, dove $a=-2$, $b=\infty $ e $c=1$

$2+\frac{-2+1}{\infty }+\frac{-3}{\infty }$

Applicare la formula: $\frac{a}{b}+\frac{c}{b}$$=\frac{a+c}{b}$, dove $a=-1$, $b=\infty $ e $c=-3$

$2+\frac{-1-3}{\infty }$

Applicare la formula: $\frac{a}{b}+\frac{c}{b}$$=\frac{a+c}{b}$, dove $a=-2$, $b=\infty $ e $c=1$

$2+\frac{-2+1}{\infty }+\frac{-3}{\infty }$

Applicare la formula: $a+b$$=a+b$, dove $a=-2$, $b=1$ e $a+b=-2+1$

$2+\frac{-1}{\infty }+\frac{-3}{\infty }$

Applicare la formula: $a+b$$=a+b$, dove $a=-1$, $b=-3$ e $a+b=-1-3$

$2+\frac{-4}{\infty }$

Applicare la formula: $a+b$$=a+b$, dove $a=-2$, $b=1$ e $a+b=-2+1$

$2+\frac{-1}{\infty }+\frac{-3}{\infty }$

Applicare la formula: $a+b$$=a+b$, dove $a=-1$, $b=-3$ e $a+b=-1-3$

$2+\frac{-4}{\infty }$

Applicare la formula: $a+b$$=a+b$, dove $a=1$, $b=-3$ e $a+b=1-3$

$2+\frac{-2}{\infty }$

Applicare la formula: $a+b$$=a+b$, dove $a=1$, $b=-3$ e $a+b=1-3$

$2+\frac{-2}{\infty }$

Applicare la formula: $a+b$$=a+b$, dove $a=-1$, $b=1$ e $a+b=-1+1$

$\frac{2+\frac{1}{\infty }+\frac{-3}{\infty }}{1+\frac{0}{\infty }}$

Applicare la formula: $\frac{a}{b}+\frac{c}{b}$$=\frac{a+c}{b}$, dove $a=1$, $b=\infty $ e $c=-3$

$\frac{2+\frac{1-3}{\infty }}{1+\frac{0}{\infty }}$

Applicare la formula: $\frac{a}{b}+\frac{c}{b}$$=\frac{a+c}{b}$, dove $a=-1$, $b=\infty $ e $c=1$

$\frac{2+\frac{1}{\infty }+\frac{-3}{\infty }}{1+\frac{-1+1}{\infty }}$

Applicare la formula: $\frac{a}{b}+\frac{c}{b}$$=\frac{a+c}{b}$, dove $a=1$, $b=\infty $ e $c=-3$

$2+\frac{1-3}{\infty }$

Applicare la formula: $\frac{a}{b}+\frac{c}{b}$$=\frac{a+c}{b}$, dove $a=1$, $b=\infty $ e $c=-3$

$2+\frac{1-3}{\infty }$

Applicare la formula: $\frac{a}{b}+\frac{c}{b}$$=\frac{a+c}{b}$, dove $a=-1$, $b=\infty $ e $c=-3$

$2+\frac{-1-3}{\infty }$

Applicare la formula: $\frac{a}{b}+\frac{c}{b}$$=\frac{a+c}{b}$, dove $a=-2$, $b=\infty $ e $c=1$

$2+\frac{-2+1}{\infty }+\frac{-3}{\infty }$

Applicare la formula: $\frac{a}{b}+\frac{c}{b}$$=\frac{a+c}{b}$, dove $a=-1$, $b=\infty $ e $c=-3$

$2+\frac{-1-3}{\infty }$

Applicare la formula: $\frac{a}{b}+\frac{c}{b}$$=\frac{a+c}{b}$, dove $a=-2$, $b=\infty $ e $c=1$

$2+\frac{-2+1}{\infty }+\frac{-3}{\infty }$

Applicare la formula: $a+b$$=a+b$, dove $a=-2$, $b=1$ e $a+b=-2+1$

$2+\frac{-1}{\infty }+\frac{-3}{\infty }$

Applicare la formula: $a+b$$=a+b$, dove $a=-1$, $b=-3$ e $a+b=-1-3$

$2+\frac{-4}{\infty }$

Applicare la formula: $a+b$$=a+b$, dove $a=-2$, $b=1$ e $a+b=-2+1$

$2+\frac{-1}{\infty }+\frac{-3}{\infty }$

Applicare la formula: $a+b$$=a+b$, dove $a=-1$, $b=-3$ e $a+b=-1-3$

$2+\frac{-4}{\infty }$

Applicare la formula: $a+b$$=a+b$, dove $a=1$, $b=-3$ e $a+b=1-3$

$2+\frac{-2}{\infty }$

Applicare la formula: $a+b$$=a+b$, dove $a=1$, $b=-3$ e $a+b=1-3$

$2+\frac{-2}{\infty }$

Applicare la formula: $a+b$$=a+b$, dove $a=-1$, $b=1$ e $a+b=-1+1$

$\frac{2+\frac{1}{\infty }+\frac{-3}{\infty }}{1+\frac{0}{\infty }}$

Applicare la formula: $a+b$$=a+b$, dove $a=1$, $b=-3$ e $a+b=1-3$

$\frac{2+\frac{-2}{\infty }}{1+\frac{0}{\infty }}$

Applicare la formula: $\frac{a}{b}$$=0$, dove $a=-2$ e $b=\infty $

$\frac{2+\frac{1}{\infty ^{2}}+\frac{-3}{\infty ^3}}{1+\frac{-1}{\infty ^{2}}+\frac{1}{\infty ^3}}$

Applicare la formula: $\frac{a}{b}$$=0$, dove $a=-2$ e $b=\infty $

$\frac{2}{1}$

Applicare la formula: $\frac{a}{b}$$=\frac{a}{b}$, dove $a=2$, $b=1$ e $a/b=\frac{2}{1}$

$2$
10

Valutare il limite $\lim_{x\to \infty }\left(\frac{2+\frac{-2}{x}+\frac{1}{x^{2}}+\frac{-3}{x^3}}{1+\frac{2}{x}+\frac{-1}{x^{2}}+\frac{1}{x^3}}\right)$ sostituendo tutte le occorrenze di $x$ con $\infty $

$2$

Risposta finale al problema

$2$

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