# hw8sol - Plug in 1 and 2 , Problem 5. a) G(x)=-(1-x 7...

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Solution to Homework 8 Problem 1. a) a 0 =-1, a 1 =2, a 2 =-4, a 3 =8, a 4 =-16, a 5 =32 b) a 0 =2, a 1 =-1, a 2 =-3, a 3 =-2, a 4 =1, a 5 =3 c) a 0 =1, a 1 =3, a 2 =27, a 3 =2187, a 4 =3 15 , a 5 =3 31 d) a 0 =-1, a 1 =0, a 2 =1, a 3 =3, a 4 =13, a 5 =74 e) a 0 =1, a 1 =1, a 2 =2, a 3 =2, a 4 =1, a 5 =1 Problem 2. a) 0=a n =-3a n-1 +4a n-2 =0+0=0=a n b) 1=a n =-3a n-1 +4a n-2 =-3*1+4*1=1=a n c) (-4) n =a n =-3*(-4) n-1 +4*(-4) n-2 =(-4) n-2 (-4*(-3)+4)=(-4) n-2 *(-4) 2 =(-4) n =a n d) 2*(-4) n +3=a n =(-3)*(2*(-4) n-1 +3)+4*(2*(-4) n-2 +3)=-6*(-4) n-1 +8*(-4) n-2 +3=3+2*(- 4) n =a n Problem 3. a) r 2 -r-6=0 => r 1 =3, r 2 =-2, m 1 =1, m 2 =1 a n = ɲ 1 r 1 n + ɲ 2 r 2 n = ɲ 1 3 n + ɲ 2 (-2) n ɲ 1 =12/5, ɲ 2 =3/5 a n =(12/5)*3 n +(3/5)*(-2) n b) r 2 -7r+10=0 => r 1 =2, r 2 =5, m 1 =1, m 2 =1 a n = ɲ 1 *2 n + ɲ 2 *5 n ɲ 1 =3, ɲ 2 =-1 a n =3*2 n -5 n c) r 2 -6r+8=0 => r 1 =2, r 2 =4, m 1 =1, m 2 =1 a n = ɲ 1 *2 n + ɲ 2 *4 n ɲ 1 =3, ɲ 2 =1 a n =3*2 n +4 n d) r 2 -2r+1=0 => r 1 =1, m 1 =2 a n =( ɲ 1,0 + ɲ 1,1 n)*1 n ɲ 1,0 =4, ɲ 1,1 =-3 a n =(4-3n) Problem 4. ܽ ݊ α ߙ ͳ ȋ ͳ Ϊ ξͷ ʹ Ȍ ݊ Ϊ ߙ ʹ ȋ ͳ ξͷ ʹ Ȍ ݊

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ܽ Ͳ α ݏ α ߙ ͳ Ϊ ߙ ʹ ܽ ͳ α ݐ α ߙ ͳ ȋ ͳ Ϊ ξͷ ʹ Ȍ Ϊ ߙ ʹ ȋ ͳ ξͷ ʹ Ȍ ݏ݋ ǡ ߙ ͳ α ݐ െ ͳ െ ξ ͷ ʹ ݏ ξ ͷ ǡ ߙ ʹ α ͳ ξ ͷ ݐ Ϊ ͳ Ϊ ξ ͷ ʹ ξ ͷ ݏ ݏ݅݊ܿ݁ ǡ ݂ α ͳ ξ ͷ ȋ ͳ Ϊ ξ ͷ ʹ Ȍ ͳ ξ ͷ ȋ ͳ െ ξ ͷ ʹ Ȍ ǡ ݂ ௡ି ͳ α ͳ ξ ͷ ȋ
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Unformatted text preview: Plug in 1 and 2 , Problem 5. a) G(x)=-(1-x 7 )/(1-x) b) G(x)=1/(1-3x) c) G(x)=3x 2 /(1+x) d) G(x)=(1+x-x 2 )/(1-x) e) G(x)=(1+2x) 7 f) G(x)=-3/(1+x) g) G(x)=x/(1+2x) h) G(x)=1/(1-x 2 ) Problem 6. a) 2G(x) b) x*G(x) c) G(x)*x 2-a x 2-a 1 x 3 d) (G(x)-a-a 1 x)/x 2...
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## This note was uploaded on 11/05/2011 for the course CSCE 222 taught by Professor Math during the Spring '11 term at Texas A&M.

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hw8sol - Plug in 1 and 2 , Problem 5. a) G(x)=-(1-x 7...

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