The root of f(x) = 4r²-3 is to be used to approximate √3/4 numerically. (i) Justify why the solution of the fixed point formula z=4r²+r-3 is a root of f(x) = 0. (ii) Determine the interval of convergence of the fixed point in (i) above.

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PLEASE NOTE: Unless otherwise stated, ALL arguments of trigonometric functions are in radians.
QUESTION 1
(a) The root of f(x) = 4r²-3 is to be used to approximate √3/4 numerically.
(i) Justify why the solution of the fixed point formula z = 4r²+r-3 is a root of f(x) = 0.
(ii) Determine the interval of convergence of the fixed point in (i) above.
(b) Perform ONE complete iteration of Newton's method for two variables for the nonlinear system
using (1, 1) as the initial solution.
xy + 2y = 1
Transcribed Image Text:PLEASE NOTE: Unless otherwise stated, ALL arguments of trigonometric functions are in radians. QUESTION 1 (a) The root of f(x) = 4r²-3 is to be used to approximate √3/4 numerically. (i) Justify why the solution of the fixed point formula z = 4r²+r-3 is a root of f(x) = 0. (ii) Determine the interval of convergence of the fixed point in (i) above. (b) Perform ONE complete iteration of Newton's method for two variables for the nonlinear system using (1, 1) as the initial solution. xy + 2y = 1
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