let′s define linear differantial operator D
as D=z∙((d )/dz)(z∙((d )/dz))+z(1−((α/z))^2 )
when
Df(z)={z∙((d )/dz)(z∙((d )/dz))+z(1−((α/z))^2 )}f(z)=0
f(z)=?
1) The function H is defined by H(x) =3cosh(x/3)+sinh(x/3).
Find the value of λ for which H(lnλ^3 )=4
2) Prove that ∫_2 ^4 ((6x+1)/((2x−3)(3x−2)))dx= ln 10.
3)Show that ((sinθ + sin2θ)/(1+ cosθ+ cos2θ))≡ tanθ
4) If z=cosθ+ i sinθ, Show that z+(1/z)=2cosθ and that
z^n +(1/z^n )=2cos nθ hence or otherwise show that
32cos^6 θ= cos 6θ +6cos 4θ + 15cos 2θ+ 10.
Mr Hans