3/5/2007
hints
1102 exercise sheet 6 Q2 see notes on 21-02-07 example2.19,
For 0<x<1 use taylor's series with remainder in Lagrange's form:=> |Rn(x)|<...<...<alpha factorial/(n+1)factorial --->0 as n--->infinity.
similarly with -1<x<0 use taylor's series with remainder in Cauchy's form.
1202 Q2(iii)
observe that ( 7 -4 ) * ( Xn ) =( Xn+1 )
6 -3 Yn Yn+1
so ( ? ? ) * ( Xo ) =( Xn )
? ? Yo Yn
and Xo=1 Yo=0.
The rest are easy enough even for a normal brain.
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