2-3x-2x^2
=-(2x^2+3x-2)
=-(2x-1)(x+2)
1/(2-3x-2x^2)=-1/[(2x-1)(x+2)]
let
-1/[(2x-1)(x+2)]≡ A/(2x-1) +B/(x+2)
=>
-1≡ A(x+2) +B(2x-1)
x=1/2 , =>A=-2/3
x=-2, => B=1/5
ie
-1/[(2x-1)(x+2)]
≡-(2/3)[1/(2x-1)] + (1/5)[1/(x+2)]
f^(n)(x) =(-1)^n. n!. { -(2/3).2^n/(2x-1)^n + (1/5)[1/(x+2)^n] }
f^(n)(0)
=(-1)^n. n!. [ -(2/3).2^n/(-1)^n + (1/5)(1/2^n) ]
=n!. [ -(2/3).2^n + (1/5)(-1)^n.(1/2^n) ]
=-(2x^2+3x-2)
=-(2x-1)(x+2)
1/(2-3x-2x^2)=-1/[(2x-1)(x+2)]
let
-1/[(2x-1)(x+2)]≡ A/(2x-1) +B/(x+2)
=>
-1≡ A(x+2) +B(2x-1)
x=1/2 , =>A=-2/3
x=-2, => B=1/5
ie
-1/[(2x-1)(x+2)]
≡-(2/3)[1/(2x-1)] + (1/5)[1/(x+2)]
f^(n)(x) =(-1)^n. n!. { -(2/3).2^n/(2x-1)^n + (1/5)[1/(x+2)^n] }
f^(n)(0)
=(-1)^n. n!. [ -(2/3).2^n/(-1)^n + (1/5)(1/2^n) ]
=n!. [ -(2/3).2^n + (1/5)(-1)^n.(1/2^n) ]