洛必达法则求极限这几个题怎么做?

2025-02-16 09:23:20
推荐回答(1个)
回答(1):

(4)=lim(x²-tan²x)/x²tan²x
=lim(x+tanx)/x lim(x-tanx)/x³
=2lim(1-sec²x)/3x²
=-2/3
(10)=lim-e(e^(ln(1+x)/x-1)-1)/x
=lim-e(ln(1+x)/x-1)/x
=lime(x-ln(1+x))/x²
=lime(1-1/(1+x))/2x
=lime/2(1+x)
=e/2
(11)=e^lim(ln(x+1)/x-lne)/x
=e^lim(ln(x+1)-x)/x²
由上
=e^(-1/2)