Question

X Solution.pdf x Solved Problems x 1 * Chapter%206.pdf 18-02-ME-GE301 " Univery macaron ROBLEM 6.11 (a) Apply the Newton-Raphson method to the function f(x) = tanh(x2 – 9) to evaluate its known real root at x = 3. Use an initial guess of Xo = 3.2 and take a minimum of three iterations. (b) Did the method exhibit convergence onto its real root? Sketch the plot with the results for each iteration labeled. Alla y PROBLEM 6.11 (a) Apply the Newton-Raphson method to the function

Answer 1

Gold I be geven equation psi fax=tanh (291=Y f'(X)=2x lechlag) formula of Newton Raphson method = Reti = Xp-f (8P) yo . f'(ap) * $(3.2) =tan n [3._2] =100845456] + C3-2)= -x 2-2 x , ” te

>> f'(3.2) –[1823611) from © =4*,=20-f(do) Qt q=0 fico) = 302–0.845456 . 1082 3511 84107 = 27368 * Error blw fost two ateratons. -) en la &a= 1 * * | *100pealehti Meroko 247368 584366-008usus X200% os lea=1659241%) for 2,24368 => FC204368) =tano [2073689-9) 70.9069])

009716 >3067019 +'(2-4368) = 2X2:4368 x[ie troet metrovez]" =lo:097164 from one = 1 =4W = 2,- Canon =)22 = 21736860.90691), =)ā_=3.67019) * Error b/w first", a terations foomes, ea = | 12-02-X1000) = 1367914 24 horof. =-) EQ=25.431%) tor 9,=3067019 f (3164019)=tan hſ3.670197 = 10.999738 f'(3.69019)= 2X 3067019x In 3067019 4-67034 G - 0346 te

3-) fl(3.67019)=0.003844] from o at p=2=4 23=0,- +(82) ang = 3.67019- 0.999738 0.003844 =>05=-2016-47) of Error ble e iterations from =) ea= | 13-14X100% =1-2576.41-3.670190 -256.41 c) Ea= 101.61314%)

.: Ea f(a) f(0) 302 0.80456 108253 2.736816 -0.90691 0.97164 3,67019 0.999738 0.003844 -215601 160924%. 21764304- 10104304 IT (3) of ois Tis I ési te dosta 015+ y =tank lama) from graph, after the real root 3, the soletton doverges-