What is the limit of $sqrt(x^3-2x^2+1)/[x-1]$ as x goes to infinity?

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Answer 1 · 2015-10-17T02:08:18

$lim_(xrarroo)sqrt(x^3-2x^2+1)/(x-1) = oo$

$sqrt(x^3-2x^2+1) = sqrt(x^2(x-2+1/x^2))$

$= sqrt(x^2)sqrt(x-2+1/x^2)$

$= absx sqrt(x-2+1/x^2)$

So

$lim_(xrarroo)sqrt(x^3-2x^2+1)/(x-1) = lim_(xrarroo)(absx sqrt(x-2+1/x^2))/(x(1-1/x))$

$= lim_(xrarroo)(sqrt(x-2+1/x^2))/(1-1/x)$

$= oo$

What is the limit of sqrt(x^3-2x^2+1)/[x-1]sqrt(x^3-2x^2+1)/[x-1] as x goes to infinity?