Question #4d075

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Answer 1 · 2017-07-11T16:25:37

Rewrite the function as follows

$f (x) = x \cdot (1 - \frac{\sqrt{x}}{x}) = x \cdot (1 - \frac{1}{\sqrt{x}})$ $f(x)=x*(1-sqrtx/x)=x*(1-1/sqrtx)$

Because $lim_(x->oo) 1/sqrtx=0$

we have that

$lim_(x->oo) f(x)=lim_(x->oo) x*(1-1/sqrtx)=oo*(1-0)=+oo$

Answer 2 · 2017-07-11T16:27:11

$lim_(x->oo) f(x)=oo$

graph{x-(sqrtx) [-16.15, 15.89, -4.17, 11.85]}

$lim_(x->oo) f(x)=oo$

As $x$ approaches $oo$ , $f(x)$ approaches $oo$ .