Chapter 12.3, Problem 46E

(a)

To determine

To show: That for the given function the potential $V$ is approximately equal to $\frac{k_2}{z}$ where $k_2$ is a constant, using Taylor polynomial of degree $1$  at $x=0$ for the function $f\left(x\right)=\sqrt{x+1}$.

(b)

To determine

To show: That for the given function the potential $V$ is approximately equal to $k_1\left(R-z+\frac{z^2}{2R}\right)$ where $k_1$ is a constant, using Taylor polynomial of degree $1$  at $x=0$ for the function $f\left(x\right)=\sqrt{x+1}$.