Trabalho sobre o metodo de newton-rapso

Método 1
Exercico 13.
Y=2x3-6x2+3x+1
A Raiz no Intevalo de [2,3] = 2,22474

Exercício 14.
Y=x4+x-4
A Raiz no Intervalo de [1,2] =1,28378.

Exercício 15.
Y=x2-sen x
A raiz positiva = 0,87673

Exercício 16.
Y=x4-2cosx
A raiz positiva = 1,01396

Lista 2
Exercício 17.
F(x)=x4-1-x

Chute Inicial=-1
Cálculos:
Convergência: f'x=ddx x4-ddx 1 – ddx x f'x= 4x3-1 f''x= 4ddxx3-ddx1 f''x= 12x2 fx*f''xf'x2<1 -14+1-1*12*(-12)4*1,220743-12<1
0,48<1

Newton-Rapson: xn+1=xn-fxnf'xn fx1=-14-1—1=1 f'x1=4-13-1=-5 x2=-1-1-5 x2=-0,8 f(x2)=-0,84-1--0,8=0,2096 f'x2=4-0,83-1=-3,048 x3=-0,8-0,2096-3,048 x3=-0,7312335958 fx3=-0,73123359584-1--0,7312335958=0,171404359 f'x3=4-0,73123359583-1=-2,56396993654 x4=-0,7312335958-0,171404359-2,56396993654 x4=-0,664382437931 fx4=-0,6643824379314-1--0,664382437931=-0,140780049815 f'x4=4-0,6643824379313-1=-2,17304432586 x5=-0,664382437931-(-0,140780049815-2,17304432586) x5=-0,729112955333 fx5=-0,7291129553334-1--0,729112955333=0,01171655207 f'x5=4-0,7291129553333-1=-2,55039985228 x6=-0,729112955333-0,01171655207-2,55039985228 x6=-0,72451894939 fx6=-0,724518949394-1--0,72451894939=0,00006804804 f'x6=4-0,724518949393-1=-2,5212802861 x7=-0,72451894939-0,00006804804-2,5212802861 x7=-0,724491959912 fx7=-0,7244919599124-1--0,724491959912=0,0000000023 f'x7=4-0,724491959912-1=-2,52111028213 x8=-0,724491959912-0,0000000023-2,52111028213 x8=-0,724491959 Exercício 18. fx= ex-3+2x
Chute Inicial= 0,5
Cálculos:
Convergência: f'x= ddx ex -ddx3+2ddxx f'x= ex+2 f''x= ddx ex+ddx2 f''x= ex fx*f''xf'x2<1 e0,5-3+2*0,5*e0,5e0,5+22<1
0,00435<1
Newton-Rapson: xn+1=xn-fxnf'xn fx1=e0,5-3+2*0,5=-0,3512787293 f'x1=e0,5+2=3,6487212787 x2=0,5--0,35127872933,6487212787 x2=0,596274476245 fx2=e0,596274476245-3+2*0,596274476245=0,00789203529 f'x2=e0,594204958514+2=3,8153430829 x3=0,596274476245-0,007892035293,8153430829
x3=0,594205971859