COMPUTE THE ROOT OF THE GIVEN FUNCTION BY NEWTON RAPHSON METHOD. f(x) = 2x^2 - ln x - 5?x i | xn | f(xn) | f'(xn) | xn+1 | REL. ERROR 1 | 3 | 8.241133673 | X1 | 2.193886423 | 2 | 2.19388642 | X2 | 6.631887116 | | 10.93958 3 | X3 | 0.108284049 | | 1.95830625 | 0.98271 4 | 1.95830625 | 0.000872003 | | | X4 5 | X5 | 5.85138E-08 | 5.535350308 | | 0.00000 COMPUTE THE ROOT WITHIN THE INTERVAL [3,4] OF THE GIVEN FUNCTION BY BISECTION METHOD. f(x) = 3x^2 - 7x - 15 i | a | b | c | f(a) | f(b) | f(c) | REL. ERROR 1 | 3 | 4 | 3.5 | -9 | 5 | -2.75 | 2 | | | | -2.75 | 5 | X1 | 6.6667 3 | 3.5 | | X2 | -2.75 | | -0.953125 | 3.4483 4 | 3.625 | | | -0.953125 | 0.9375 | -0.01953125 | X3 5 | | | | | 0.9375 | 0.456054688 | X4 6 | 3.6875 | X5 | | -0.01953125 | 0.456054688 | 0.217529297 | 0.4219 7 | 3.6875 | 3.703125 | 3.6953125 | | | 0.098815918 | 0.2114 8 | | | X6 | -0.01953125 | 0.098815918 | 0.039596558 | 0.1058 9 | 3.6875 | | | -0.01953125 | 0.039596558 | 0.01002121 | 0.0529 10 | | | X7 | -0.01953125 | 0.01002121 | -0.004757881 | 0.0265
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The method involves the following formula: xn+1 = xn - f(xn)/f'(xn) where xn is the current approximation of the root, xn+1 is the next approximation, f(xn) is the value of the function at xn, and f'(xn) is the derivative of the function at xn. To apply this Show more…
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