Chapter 8.1, Problem 46E

To determine

(a)

To graph:

The curves with equations $x^n+y^n=1,n=\mathrm{2,4},\mathrm{6,8},10$

To determine

(b)

To set up:

An integral for the length $L_{2k}$ of the fat circle with $n=2k$

To determine

(c)

To state:

The value of $\underset{k\to \infty }{\lim }{L}_{2k}$