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2. (a) For the equation e^x = 3 - 2 x , find a function, f(x),...

2. (a) For the equation e^x = 3 - 2 x , find a function, f(x), whose x-intercept is the solution of the equation (i.e. a function suitable to use in Newton’s Method), and use it to set up xn+1 for Newton’s Method.

(b) Use Newton's method to find x3 , x4 and x5 using the initial guess x1 = 0 . How many digits of accuracy are you certain of from these results?

(c) Use x1+ ln 2   and show that Newton’s Method fails in this case. Explain why this happens in terms of the the tangent lines of f(x).

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