Problem

A method of finding a zero of a given function f proceeds as follows. Two initial approx...

A method of finding a zero of a given function f proceeds as follows. Two initial approximations x₀ and x₁ to the zero are chosen, the value of x₀ is fixed, and successive iterations are given by

This process will converge to a zero of f under certain conditions. Show that the rate of convergence to a simple zero is linear under some conditions.

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Solutions For Problems in Chapter 3.3

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