Find the positive root of the equation 3x+sinx-ex using Regula Falsi method and correct upto 4 decimal places.

f(0) = -1f(1) = 1.123189156Therefore, root lies between 0 and 1a = 0; f(a) = -1b = 1; f(b) = 1.123189156Substituting the values in the FORMULA,x = \(\frac{bf(a)-af(b)}{f(a)-f(b)} \),we get \(x1 = \frac{-1}{-1-1.123189156}\)=0.470989594; f(x1) = 0.265158816Therefore, x1 becomes b to find the next point.\(X2 = \frac{-0.470989594}{-1-0.265158816}\)=0.372277051; f(x2) = 0.029533668Therefore, x2 becomes b to find the next point.\(X3 = \frac{-0.029533668}{-0.029533668-1}\)=0.361597743; f(x3) = 2.940998193*10-3Therefore, x3 becomes b to find the next point.\(X4 = \frac{-0.361597743}{-1-(2.940998193*10^{-3})}\)=0.360537403; f(x4) = 2.89448416*10-3Therefore, x4 becomes b to find the next point.\(X5 =\frac{-0.360537403}{-1-(2.89448416*10^{-3})}\)=0.360433076; f(x5) = 2.84536596 * 10-5Therefore x5 becomes b to find the next point.\(X6 = \frac{-0.360433076}{-1-(2.84536596*10^{-5})}\)=0.36042282Therefore, the positive root corrected to 4 decimal places is 0.3604.