List of top Engineering Mathematics Questions on Numerical Methods asked in GATE TF

The value of \( \alpha \) for which the Euler method with step size \( h = 0.1 \) provides \( y(1.1) = 1.2 \) for the following initial value problem is \[ \frac{dy}{dx} = -2xy^\alpha, \quad y(1) = 2 \]
If the values of $x$ are 1, 2, and 3 and the corresponding values of $y$ are 9, 8, and 10 respectively, then the slope of the line of regression equation of $y$ on $x$ is (up to 1 decimal place) __________________.