Impara online a risolvere i problemi di prodotti speciali passo dopo passo. (x)->(infinito)lim(((x+1)^(1/2)-1)/((x+1)^(1/3)-1)). Applicare la formula: \lim_{x\to c}\left(\frac{a}{b}\right)=\lim_{x\to c}\left(\frac{\frac{a}{sign\left(c\right)fgrow\left(b\right)}}{\frac{b}{sign\left(c\right)fgrow\left(b\right)}}\right), dove a=\sqrt{x+1}-1, b=\sqrt[3]{x+1}-1, c=\infty , a/b=\frac{\sqrt{x+1}-1}{\sqrt[3]{x+1}-1} e x->c=x\to\infty . Applicare la formula: \lim_{x\to c}\left(\frac{a}{b}\right)=\lim_{x\to c}\left(\frac{radicalfrac\left(a\right)}{radicalfrac\left(b\right)}\right), dove a=\frac{\sqrt{x+1}-1}{\sqrt[3]{x+1}}, b=\frac{\sqrt[3]{x+1}-1}{\sqrt[3]{x+1}} e c=\infty . Applicare la formula: \lim_{x\to c}\left(\frac{a}{b}\right)=\lim_{x\to c}\left(\frac{splitfrac\left(a\right)}{splitfrac\left(b\right)}\right), dove a=\sqrt[3]{\frac{x+1}{\left(\sqrt{x+1}-1\right)^{3}}}, b=\sqrt[3]{\frac{x+1}{\left(\sqrt[3]{x+1}-1\right)^{3}}} e c=\infty . Valutare il limite \lim_{x\to\infty }\left(\frac{\sqrt[3]{\frac{x}{\left(\sqrt{x+1}-1\right)^{3}}+\frac{1}{\left(\sqrt{x+1}-1\right)^{3}}}}{\sqrt[3]{\frac{x}{\left(\sqrt[3]{x+1}-1\right)^{3}}+\frac{1}{\left(\sqrt[3]{x+1}-1\right)^{3}}}}\right) sostituendo tutte le occorrenze di x con \infty .

(x)->(infinito)lim(((x+1)^(1/2)-1)/((x+1)^(1/3)-1))