Answer to Question #142196 in Quantitative Methods for Mehwish

Question #142196
2 Find the root of the equation xex = cosx in the interval (0, 1) using
Regula-Falsi method correct to four decimal places.
1
Expert's answer
2020-11-03T18:30:23-0500

"\\displaystyle\n\n\nxe^x = \\cos{x}\\\\\n\nf(x) = xe^x - \\cos{x}\\\\\n\n\nf(0.5) = 0.5e^{0.5} - \\cos{0.5} = -0.0532 < 0\\\\\n\n\nf(0.6) = 0.6e^{0.6} - \\cos{0.6} = 0.2679 > 0\\\\\n\n\n\n\\textsf{By Regula-Falsi method}\\\\\n\n\n\nx_1 = \\frac{0.5 f(0.6) - 0.6f(0.5)}{f(0.6) - f(0.5)} = 0.5165719036 \\\\\n\n\nf(0.5165719036) < 0\\\\\n\nf(0.6) > 0\\\\\n\n\n\n\\textsf{Repeating the process}\\\\\n\nx_2 = \\frac{0.6f(0.5165719036 ) - 0.5165719036 f(0.6)}{f(0.5165719036) - f(0.6)} = 0.51767881731\\\\\n\n\n\n\\therefore x = 0.5177 \\, \n\\, \\textsf{(to 4.d.p)}"


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