Question

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

Answer 1

`x-sqrtx = sqrtx(sqrtx-1)`

Explanation:

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

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