How do I calculate this?

Question

How do I calculate the limit of x- #sqrt(x)# where x is nearing to infinity

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Answer 1 · 2017-09-22T10:27:11

#lim_"x->oo" (x-sqrtx) = oo#

#f(x) = x-sqrtx#

#= x(1-1/sqrtx)#

#:.lim_"x->oo" f(x) = lim_"x->oo" x xx lim_"x->oo" (1-1/sqrtx)#

Now consider #lim_"x->oo" (1-1/sqrtx) = 1-0 =1#

Hence, #lim_"x->oo" f(x) = lim_"x->oo" x xx 1 = oo#