dany jest wielomian W Oblicz w [-1] W[0] W[1] gdy; W[x]=-1/3xdo 6-1/2xdo3+3xdo2+6 W[x]=3/4xdo7-1/3xdo5+3xdo2+2x

dany jest wielomian W Oblicz w [-1] W[0] W[1] gdy; W[x]=-1/3xdo 6-1/2xdo3+3xdo2+6 W[x]=3/4xdo7-1/3xdo5+3xdo2+2x
Odpowiedź

[latex]W(x)=-frac{1}{3}x^{6}-frac{1}{2}x^{3}+3x^{2}+6[/latex]   [latex]W(-1)=-frac{1}{3}*(-1)^{6}-frac{1}{2}*(-1)^{3}+3*(-1)^{2}+6=[/latex] [latex]=-frac{1}{3}+frac{1}{2}+3+6=-frac{2}{6}+frac{3}{6}+9=9frac{1}{6}[/latex]   [latex]W(0)=-frac{1}{3}*(0)^{6}-frac{1}{2}*(0)^{3}+3*(0)^{2}+6=6[/latex]   [latex]W(1)=-frac{1}{3}*(1)^{6}-frac{1}{2}*(1)^{3}+3*(1)^{2}+6=-frac{1}{3}-frac{1}{2}+3+6= [/latex] [latex]=-frac{2}{6}-frac{3}{6}+9=-frac{5}{6}+9=8frac{1}{6}[/latex]   ;)

W(x) = ( -1/3) x^6 - (1/2) x^3 + 3 x^2 + 6 zatem W(-1) = ( - 1/3)*1 - ( 1/2)*(-1) + 3*1 + 6 = - 2/6 + 3/6 + 9 =  9  1/6 W(0) = ( -1/3)*0 - (1/2)*0 + 3*0 + 6 = 6 W(1) = ( -1/3)*1 - (1/2)*1 + 3*1 + 6 = - 2/6 - 3/6 + 9 = 9 - 5/6 = 8  1/6 =============================================================== W(x) = ( 3/4) x^7 - (1/3) x^5 + 3 x^2 + 2 x zatem W(-1) = ( 3/4)*( -1) - (1/3)*(-1) + 3*1 + 2*(-1) = - 3/4 + 1/3 + 3 - 2 =          = - 9/12 + 4/12 + 1 = 1 - 5/12 = 7/12 W( 0) = ( 3/4)*0 - (1/3)*0 + 3*0 + 2*0 = 0 W( 1) = (3/4)*1 - (1/3)*1 + 3*1 + 2*1 = 3/4 - 1/3 + 3 + 2 =          =  9/12 - 4/12 + 5 = 5/12 + 5 = 5  5/12 ================================================

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