Apply the central difference formula (4.10) to approximate the first derivatives of the functions \(u_{1}(x)=\sin (x), u_{2}(x)=\sin (3 x)\), \(u_{3}(x)=\sin (10 x)\) at \(x=0\). Use the uniform grid with step \(\Delta x=0.1\). Compare the results with the exact values of the derivatives, and explain why the error of approximation is different for the three functions.