求lim(√x^2+1)-xx→-∞

Question

求lim(√x^2+1)-x x→-∞

Answer 1

如果是负无穷
lim(√x^2+1)是正的
x x是负的
结果为无穷大
如果x趋于正无穷
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