f(x)=e^x(x^3+x^2+x-1)在x趋向负无穷的极限怎么求要过程.
2019-06-02
f(x)=e^x(x^3+x^2+x-1)在x趋向负无穷的极限怎么求要过程.
优质解答
f(x)=(x^3+x^2+x-1)/e^(-x)
可用罗比达法则,既分子分母分别求导
lim(x^3+x^2+x-1)/e^(-x)
=(3x^2+2x+1)/-e^(-x)
=(6x+2)/e^(-x)
=6/-e^(-x)
x趋于负无穷时,e^(-x)趋于无穷大
故limf(x)(x→负无穷)=0
f(x)=(x^3+x^2+x-1)/e^(-x)
可用罗比达法则,既分子分母分别求导
lim(x^3+x^2+x-1)/e^(-x)
=(3x^2+2x+1)/-e^(-x)
=(6x+2)/e^(-x)
=6/-e^(-x)
x趋于负无穷时,e^(-x)趋于无穷大
故limf(x)(x→负无穷)=0