5. (5 points) The total magnetic moment in the direction of the field acquired by the unit volume under consideration, that is, the magnetization M, is M=\frac{n \mu \int_{1}^{-1} x

e^{a x} d x}{\int_{1}^{-1} e^{a x} d x} =n \mu\left(\frac{e^{a}+e^{-a}}{e^{a}-e^{-a}}-\frac{1}{a}\right)=n \mu\left(\operatorname{coth} a-\frac{1}{a}\right) (a) Give the magnetization M normalized by Mo, which is the Langevin function. (b) Plot M/Mo as a function of a (=µH/kT). (c) Plot M/Mo as a function of a (=µH/kT) for a < 0.5.