(a) Apply the Newton-Raphson method to the function f (x) = tanh(x^2 − 9) to evaluate its known real root at x = 3. Use an initial guess of x_0 = 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.

Ajournal bearing has a journal diameter of 3.250 in with a unilateral tolerance of 20.003 in. the bushing bore has a diameter of 3.256 in and a unilateral tolerance of 0.004 in. the bushing is 2.8 in long and supports a 700-lbf load. the journal speed is 900 rev/min. find the minimum oil film thickness and the maximum film pressure for both sae 20 and sae 20w-30 lubricants, for the tightest assembly if the operating film temperature is 160°f. a computer code is appropriate for solving this problem.