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Newton's method: For a function ?(?)=ln?+?2−3f(x)=ln⁡x+x2−3 a. Find the root of function ?(?)f(x) starting with ?0=1.0x0=1.0....

Newton's method: For a function ?(?)=ln?+?2−3f(x)=ln⁡x+x2−3

a. Find the root of function ?(?)f(x) starting with ?0=1.0x0=1.0.

b. Compute the ratio |??−?|/|??−1−?|2|xn−r|/|xn−1−r|2, for iterations 2, 3, 4 given ?=1.592142937058094r=1.592142937058094. Show that this ratio's value approaches |?″(?)/2?′(?)||f″(x)/2f′(x)| (i.e., the iteration converges quadratically). In error computation, keep as many digits as you can.

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