Question

求极限.lim x(根号下(x^2+1) ) -x x趋向无穷大

Answer 1

原式=lim(x->∞) [根号下(x²+1) -x]*[根号下(x²+1) ) +x]/[根号下(x²+1) ) +x]

=lim(x->∞) [(x²+1) -x²]/[根号下(x²+1) ) +x]

=lim(x->∞) 1/[根号下(x²+1) ) +x]

=0