Figure 430 shows the idea. We assume that f is continuous. We compute the x-intercept c 0

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Figure 430 shows the idea. We assume that f is continuous. We compute the x-intercept cof the line through (α0,f(α0)), (b0, f(b0)). If f(c0) = 0, we are done. If f(α0)f(c0) < 0 (as in Fig. 430), we set α1= α0, b1= c0 and repeat to get c1, etc. If f(α0)f(c0) > 0, then f(c0)f(b0) < 0 and we set α1= c0, b1= b0, etc.

(a) Show that

aof (bo) – bo f(ao) f(bo) – f(ao) Co

and write an algorithm for the method.

(b) Solve x4 = 2, cos x = √x, and x + ln x = 2, with α = 1, b = 2.

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