What is the limit of $(x-x^(1/2))$ as x goes to infinity?

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Answer 1 · 2015-10-19T19:40:10

$x-sqrtx = sqrtx(sqrtx-1)$

Since both factor increase without bond as $x$ increases without bound, we get

$lim_(xrarroo)(x-sqrtx) = lim_(xrarroo)(sqrtx(sqrtx-1)) = oo$

What is the limit of (x-x^(1/2)) (x-x^(1/2)) as x goes to infinity?