Let $f$ satisfy $\dfrac{dy}{dx} = \dfrac{1}{x}$ with $f(1) = 2$. Using Euler's method with two steps of size $1$, approximate $f(3)$.

Core Concept

At $(1,2)$ the slope is $1$, giving $y=3$ at $x=2$; at $(2,3)$ the slope is $\dfrac{1}{2}$, so the second step gives $3 + 1\cdot\dfrac{1}{2} = 3.5$.