Chapter 9.10, Problem 28E

a)

To determine

Find the polynomial to approximate the integral function ${\displaystyle {\int }_0^x\frac{\ln \left(1+t\right)}{t}}dt$ in the interval of $\left[0,0.5\right]$ with the magnitude error less than ${10}^{-3}$.

b)

To determine

Find the polynomial to approximate the integral function ${\displaystyle {\int }_0^x\frac{\ln \left(1+t\right)}{t}}dt$ in the interval of $\left[0,1\right]$ with the magnitude error less than ${10}^{-3}$.