a) Find the missing terms from the following data: \begin{tabular}{c|…

Previous year question for Numerical Methods & Transform Calculus.

Question

a) Find the missing terms from the following data:

\begin{tabular}{c|cccccccc}

$x$ & 2 & 2.1 & 2.2 & 2.3 & 2.4 & 2.5 & 2.6 \\

\hline

$y$ & 0.135 & \dots & 0.111 & 0.1 & \dots & 0.082 & 0.074

\end{tabular}

b) Using the method of false position, find a real root of $xe^x = 3$ correct to three decimal places.

c) Using Eular's method, evaluate $y(0.1)$ for $\frac{dy}{dx} = x + y + xy$ with $y(0) = 1$, taking $h = 0.025$.