Given $w^{\prime }\left(s\right)=\frac{s}{w}$, and $w\left(0\right)=5$, use Euler's method with $\Delta s=0.25$ to approximate $w\left(1\right)$. The exact solution is $w\left(s\right)=\sqrt{s^2+25}$. What is the error at $s=1$?

• A. $w\left(1\right)\approx 5.1209$$\text{Error}=0.0244$
• B. $w\left(1\right)\approx 5.1209$$\text{Error}=0.0219$
• C. $w\left(1\right)\approx 5.0746$$\text{Error}=0.0244$
• D. $w\left(1\right)\approx 5.0746$$\text{Error}=0.0219$