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[S]maggie

1. let y=sin(nshin^-1x)
a). prove that (1-x^2)y''-xy'+n^2y=0
b). hence deduce that
(1-x^2)y^(m+2)-(2m+1)xy^(m+1)+(n^2-m^2)y^(m)=0
for any positive integer m.
2.
a). let y= e^(xcotp)sin(x+Q) (p,q are constans)
i)find y' and y''
ii)prove by induction
y^(n)=[[e^(xcotp)]/[sin^(n)p]]Xsin(np+x+q) n=0,1,2,....
b).find the 40-th derivative of
F(x)=(1/2)[e^x+e^(-x)]cosx.


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