How do you find #lim x-sqrtx# as #x->oo#?

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Answer 1 · 2017-02-04T23:59:15

#lim_(x->oo) (x-sqrt(x)) = +oo#

Write the function as:

#f(x) = x-sqrt(x) = sqrt(x) (sqrt(x) -1)#

As:

#lim_(x->oo) sqrt(x) = +oo#

and

#lim_(x->oo) sqrt(x)-1 = +oo#

then also:

#lim_(x->oo) sqrt(x)(sqrt(x)-1) = +oo#