Question

高等数学问题求解答！

Answer 1

z=lncos(y/x)
dz= [1/cos(y/x)] .[-sin(y/x)][ (1/x)dy - (y/x^2) dx]
dz|(x,y) = (1,π/4)
= [1/cos(π/4)] .[-sin(π/4)][ dy - (π/4) dx ]
=-[ dy - (π/4) dx ]

追问

这题会吗？

追答

1/u =a/(2a+x)
lim(x->∞) [ (3a+x)/(2a+x) ]^x
=lim(x->∞) [ 1+ a/(2a+x) ]^x

=lim(u->∞) [ 1+ 1/u ]^(au-2a)
=lim(u->∞) [ 1+ 1/u ]^(au)
=e^a
=>
3=e^a
a=ln3

追问

谢谢

这题怎么写？

追答

∫(0->1/2) x^3/√(1-x^2) dx
=-∫(0->1/2) x^2 d√(1-x^2)
=- [x^2.√(1-x^2) ]|(0->1/2) +2∫(0->1/2) x.√(1-x^2) dx
=-√3/8 -∫(0->1/2) √(1-x^2) d(1-x^2)
=-√3/8 - (2/3)[ (1-x^2)^(3/2)]|(0->1/2)
=-√3/8 - (2/3) [ (3/4)^(3/2) -1 ]
=-√3/8 - (2/3) [ 3√3/8 -1 ]
=2/3 -√3 . ( 1/8 + 1/4)
=2/3 -(3/8)√3

追问

这三题会写吗 老师 求解答

追答

f(x) = (sinx)^2 .(x^3+ arctanx)

f(-x) =-f(x)
∫(-1->1) (sinx)^2 .(x^3+ arctanx) dx =0

追问

还有两个

谢谢老师