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**Unformatted text preview: **estimate: x2 = x1 – f(x1) f ’(x1) Repeated application of this process is called Newton’s Method. Each successive application of this procedure is called an iteration . Newton’s Method for Approximating the Zeros of a Function 1. Make an initial estimate x1 that is “close to” c. (A graph is helpful.) 2. Use the first approximation to get a second, the second to get a third, and so on, using xn+1 = xn – f(xn) f ’(xn) Defn: Differentials Let y = f(x) be differentiable function. The differential dx is an independent variable. The differential dy is ( ) dy f x dx ′ = Differential Estimate of Change ( ) df f a dx ′ = Change in f True Estimated Absolute Change Relative Change Percentage Change ( ) ( ) f f a dx f a ∆ = +-( ) df f a dx ′ = ( ) f f a ∆ ( ) df f a 100 ( ) f f a ∆ • 100 ( ) df f a • Joke Time Who was the dancing Vice-President in 2000? Al-gore rhythum What does a lumberjack do to trees? axi-oms...

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