^^=lim(e^(x²ln(1+1/x))-e^x)/x
=lime^x(e^(x²ln(1+1/x)-x)-1)/x
=lim(x²ln(1+1/x)-x)/xe^(-x)
=lim(xln(1+1/x)-1)/e^(-x)
=lim(ln(1+1/x)+x(-1/x²)/(1+1/x))/-e^(-x)
=lim(ln(1+1/x)-1/(1+x))/-e^(-x)
=lim(-1/x(1+x)+1/(1+x)²)/e^(-x)
=lim-e^x/x(1+x)²
=-∞
扩展资料
lim(x→∞)x^2/e^x怎么算高数极限
用洛毕塔
lim(x→∞)x^2/e^x
=lim(x→∞)2x/e^x
=lim(x→∞)2/e^x
=0