1. ## Re: Limit

PS: Struggling with this one isn't a sign of "sucking a bit". It's a tough one to get out whichever way you choose.

2. ## Re: Limit

Originally Posted by Archie
PS: Struggling with this one isn't a sign of "sucking a bit". It's a tough one to get out whichever way you choose.
Okay. Idk how, but now i can read it! Thank you so much... Gonna find out why i got stucked with this limit for so long!
Huge hug bro!

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4. ## Re: Limit

to simplify the calculations, write

$\displaystyle \sqrt[3]{\frac{5x^3-x^4}{x-1}}+x=x\left(\sqrt[3]{\frac{5-x}{x-1}}+1\right)$

and use the substitution

$\displaystyle y=\sqrt[3]{\frac{5-x}{x-1}}$ so that $\displaystyle x=\frac{y^3+5}{y^3+1}$

and

$\displaystyle \sqrt[3]{\frac{5x^3-x^4}{x-1}}+x=\frac{y^3+5}{y^3+1}(y+1)=\frac{y^3+5}{y^2-y+1}$

now take the limit as $y\to -1$

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