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1 Answer
Cesareo R. · Truong-Son N.
Oct 27, 2017

#0#

Explanation:

#(-3sqrtx+x^-1)/(-5x+4) =(-3x^(3//2)+1)/(-5x^2+4x) = x^(3//2)/(x^2)((-3+1/x^(3//2))/(-5+4/x)) =( 1/x^(1//2))((-3+1/x^(3//2))/(-5+4/x))#

then

#lim_(x->oo)(-3sqrtx+x^-1)/(-5x+4) =lim_(x->oo)( 1/x^(1//2))lim_(x->oo)((-3+1/x^(3//2))/(-5+4/x)) = 0 * (3/5) = 0#

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