(a) Using Regula-Falsi method, find a real root of $e^x - x^3 = 0$ be…

Previous year question for Numerical Methods & Transform Calculus.

Question

(a) Using Regula-Falsi method, find a real root of $e^x - x^3 = 0$ between $1.75$ and $2$ correct to four decimal places.

(b) Compute $y(0.3)$ by using Euler's modified method for the initial value problem $\frac{dy}{dx} = 1 - y, y(0) = 1$.

(c) Show that $\Delta = E\Delta = \Delta E = \delta E_{1/2}$.

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