NewtonRaphson@ x0_, max_D :=ModuleB8

Plot@f@xD, 8x, -5, 5

p0 = 0.0000000000000000, f@p0D =1.

p1 = 0.5000000000000000, f@p0D =0.01134878145880891

p= 0.5057395273712173,f@pD=0.01134878145880891

2 p= 0.5346911095406560,f@2 pD=0.00947116374420509

3 p= 0.5457466521293517,f@3 pD=0.002617255170712596

4 p= 0.5541878772558704,f@4 pD=0.001133153989021973

5 p= 0.5590501528340384,f@5 pD=0.0004141546717236766

6 p= 0.5621529447902443,f@6 pD=0.0001613339470762365

p =0.5621529447902443

Dp =0.00310279

f@pD =0.0000612722666615273

NewtonError = 0.567143 - 0.5559645425958832

0.0111785

SecantError = 0.567143 - 0.5621529447902443

0.00499006

f@x_D := Log@x - 1D + Cos@x - 1D

Plot @ f@xD, 8x, -5, 5

P1= 1.0460558073763590,f@P1D=-2.078961795238372

P2= 1.1420075261956400,f@P2D=-0.961941356829404

P3= 1.2814122543706730,f@P3D=-0.3072703918061856

P4= 1.3752125652068680,f@P4D=-0.04983282895852758

P5= 1.3968914012446590,f@P5D=-0.001825497071324955

P6= 1.3977472256235330,f@P6D=-2.659228743651099 10-6

p =1.397747225623533

Dp =-+0.000855824

f@pD =-2.659228743651099 10-6

FindRoot@Log@x - 1D + Cos@x - 1D, 8x, 10

Plot@f@xD, 8x, -5, 5

p0 = 1.0000000000000000, f@p0D =-4.

p1 = 3.0000000000000000, f@p0D =692.

p= 1.0114942528735630,f@pD=692.

2 p= 1.0219896114927700,f@2 pD=-3.67176441877633

3 p= 1.1353784006454350,f@3 pD=-3.36069569018272

4 p= 1.1143986026142000,f@4 pD=0.7629854624408345

5 p= 1.1171060194827600,f@5 pD=-0.1130514787912595

6 p= 1.1171816561283400,f@6 pD=-0.00307246504254266

p =1.11718165612834

Dp =0.0000756366

f@pD =0.00001291702121619664

NewtonError = 1.11718 - 1.117320727356156

-0.000140727

SecantError = 1.11718 - 1.11718165612834

-1.65613 10-6

6 Jamal_Mesidor_Newton_Secant_Method_HW_000-05-7204.nb