Which statement best describes the accuracy of Euler’s method for solving initial value problems?

Euler’s method can be applied to approximate the solution of the initial value problem $y^{\prime }\left(t\right)=t+y$, $y\left(0\right)=2$ on the interval $[0,0.3]$ with a uniform grid: $t_0=0$, $t_1=0.1$, $t_2=0.2$, $t_3=0.3$. Find the value of $u_1$ after the first Euler step.

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 $s=1$?

Determine $u_{k+1}$ in terms of $a,h,$ and $k$ when Euler’s method with step size $h$ is applied to the initial value problem $y^{\prime }\left(t\right)=a{t}^2$, $y\left(0\right)=1$ with grid points $t_k=kh$ and Euler approximations $u_k$ to $y\left(t_k\right)$.

Apply Euler's method with $\Delta x=0.25$ to approximate $y\left(1\right)$ for the IVP $y^{\prime }=x\sin y$, $y\left(0\right)=\frac{\pi }{6}$. Round Euler's approximation to $4$ decimal places. Also, determine the exact value of $y\left(1\right)$.