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# C3 - Numerical methods watch

1. The straight line with equation x+y=2 crosses the curve with equation y=3lnx, x > 0, at the point P.

(a) Show that the x-coordinate of P satisfies the equation x = e^(2-x/3)

Done that.

An approximation to the solution of this equation is to be found using the iterative formula

xn+1 = e^(2-xn/3), x0=1 (Sorry for bad formatting)

(b) Write down the values of x1 and x2, giving your answers to 5 significant figures.

x1=1.3956
x2=1.2232

(c) Show sufficient working to prove that the x-coordinate of P is 1.274, correct to 4 s.f.

Not sure how to go about doing part (c). Don't I need to sub in x as 1.2735 and 1.2745? Not sure where to sub that in to.
2. (Original post by Dan___V)
Not sure how to go about doing part (c). Don't I need to sub in x as 1.2735 and 1.2745? Not sure where to sub that in to.
If you have any (*) function f, and f changes sign between a and b (i.e. f(a)f(b) < 0), then f(x) has a root between a and b.

In this case, define f(x) = x - e^(2-x/3), a = 1.2735, b = 1.2745

(*) Well, f has to be continuous, but I *think* you can take this as a given at A-level.

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