三.
1.
原式=lim(x→无穷)(2+1/n+1/n^2)/(1/n^2+1-2/n)
=lim(x→无穷)2/1=2
4.
lim(x→0)(1+x)^(2/x)
=lim(x→0)(1+x)^(1/x)(2)
=e^2
6.
lim(x→π/2)lnsinx/(π-2x)^2
=lim(x→π/2)[cosx/sinx]/2(π-2x)(-2)
=(-1/4)lim(x→π/2)[cotx]/(π-2x)
=(-1/4)lim(x→π/2)[-csc^2x]/(-2)
=(-1/4)lim(x→π/2)[-1]/(-2)
=-1/8
四.
1.
y=sinxlnx^2
y'=cosxlnx^2+sinx(2/x)
2.
lny=cosxlna
(1/y)y'=-sinxlna+cosx/a
y'=(a^cosx)[-sinxlna+cosx/a]
3.
y=ln(x-cos3x)
y'=[1/(x-cos3x)](1+3sin3x)
4.
y=3a^x+e^x-2/x
y'=3a^xlna+e^x+2/x^2