Question #4d075

2 Answers

Rewrite the function as follows

#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#

Jul 11, 2017

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

Explanation:

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#.