Question

1 Find a real root of the equation 3x + sinx − e
x = 0 by the method of
false position correct to four decimal places.

Answer 1

$\displaystyle f(x) = 3x + \sin{x} − e^x = 0\\ f(0.3) =3(0.3) + \sin(0.3) − e^{0.3} = -0.15433860091 < 0\\ f(0.4) =3(0.4) + \sin(0.4) − e^{0.4} = 0.09759364467 > 0\\ \textsf{By Regula-Falsi method}\\ x_1 = \frac{0.3f(0.4) - 0.4f(0.3)}{f(0.3) - f(0.4)} = 0.36126194787\\ f(0.36126194787) > 0\\ f(0.3) < 0\\ \textsf{Repeating the iteration process}\\ x_2 = \frac{0.3f(0.36126194787) - 0.36126194787f(0.3)}{f(0.36126194787) - f(0.3)} = 0.3604389982\\ \therefore x = 0.3604 \, \, \textsf{(to 4 d.p.)}$