MathDB

2016 Calculus Tiebreaker #2

Source:

August 8, 2022

2016Calculus Tiebreaker

Problem Statement

Consider the curves with equations

x^n+y^n=1

for

n=2,4,6,8,\dots

. Denote

L_{2k}

the length of the curve with

n=2k

. Find

\lim_{k\rightarrow\infty}L_{2k}