Q. 15 - Calculus

Question

Explain how equality ${\left.\frac{dy}{dx}\right|}_{\left(x_k,y_k\right)}=\frac{\mathrm{\Delta }{y}_k}{\mathrm{\Delta }x}$ is relevant to Euler’s method. 

Step-by-Step Solution

Answer

Ans:    It is Proved that ${\left.\frac{dy}{dx}\right|}_{\left(x_k,y_k\right)}=\frac{\mathrm{\Delta }{y}_k}{\mathrm{\Delta }x}$  is relevant to Euler’s method. 

Step 1. Given information.

given,

    ${\left.\frac{dy}{dx}\right|}_{\left(x_k,y_k\right)}=\frac{\mathrm{\Delta }{y}_k}{\mathrm{\Delta }x}$

Step 2. Solution: