Answer to Question #142193 in Quantitative Methods for Mehwish

Question #142193
1 Find a real root of the equation 3x + sinx − e
x = 0 by the method of
false position correct to four decimal places.
1
Expert's answer
2020-11-03T18:15:43-0500

"\\displaystyle\n\n\nf(x) = 3x + \\sin{x} \u2212 e^x = 0\\\\\n\nf(0.3) =3(0.3) + \\sin(0.3) \u2212 e^{0.3} = -0.15433860091 < 0\\\\\n\n\nf(0.4) =3(0.4) + \\sin(0.4) \u2212 e^{0.4} = 0.09759364467 > 0\\\\\n\n\\textsf{By Regula-Falsi method}\\\\\n\nx_1 = \\frac{0.3f(0.4) - 0.4f(0.3)}{f(0.3) - f(0.4)} = 0.36126194787\\\\\n\n\nf(0.36126194787) > 0\\\\\n\nf(0.3) < 0\\\\\n\n\n\\textsf{Repeating the iteration process}\\\\\n\nx_2 = \\frac{0.3f(0.36126194787) - 0.36126194787f(0.3)}{f(0.36126194787) - f(0.3)} = 0.3604389982\\\\\n\n\n\\therefore x = 0.3604 \\, \\, \\textsf{(to 4 d.p.)}"


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