1.设y^(n-1)=e^x+cos2x,求y^(n+1)2.lim (x-π/2)cot2xx→π/2

1.设y^(n-1)=e^x+cos2x,求y^(n+1)2.lim (x-π/2)cot2xx→π/2
1.设y^(n-1)=e^x+cos2x,求y^(n+1)
2.lim (x-π/2)cot2x
x→π/2

1.设y^(n-1)=e^x+cos2x,求y^(n+1)2.lim (x-π/2)cot2xx→π/2
1.设y^(n-1)=e^x+cos2x,
∴y^(n)=e^x-2sin2x,
y^(n+1) =e^x+4cos2x.
2.lim < x→π/2> (x-π/2)cot2x
=lim < x→π/2> (x-π/2)/tan2x
=lim < x→π/2>1/[2(sec2x)^2]
=1/2.