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Question Number 143013 by Study last updated on 08/Jun/21

lim_(x→∞) (((x+1))^(1/3) /(x+1))=?

$${li}\underset{{x}\rightarrow\infty} {{m}}\frac{\sqrt[{\mathrm{3}}]{{x}+\mathrm{1}}}{{x}+\mathrm{1}}=? \\ $$

Commented by Study last updated on 08/Jun/21

what is the practice?

$${what}\:{is}\:{the}\:{practice}? \\ $$

Commented by Dwaipayan Shikari last updated on 08/Jun/21

0

$$\mathrm{0} \\ $$

Commented by Dwaipayan Shikari last updated on 08/Jun/21

(((x+1))^(1/3) /(x+1))  =(1/((x+1)^(2/3) ))    x is very large so (1/((x+1)^(2/3) ))→0

$$\frac{\sqrt[{\mathrm{3}}]{{x}+\mathrm{1}}}{{x}+\mathrm{1}}\:\:=\frac{\mathrm{1}}{\left({x}+\mathrm{1}\right)^{\mathrm{2}/\mathrm{3}} }\:\: \\ $$$${x}\:{is}\:{very}\:{large}\:{so}\:\frac{\mathrm{1}}{\left({x}+\mathrm{1}\right)^{\mathrm{2}/\mathrm{3}} }\rightarrow\mathrm{0} \\ $$

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