Concept explainers
Extreme points on flattened spheres The equation x2n + y2n +z2n = 1, where n is a positive integer, describes a flattened sphere. Define the extreme points to be the points on the flattened sphere with a maximum distance from the origin.
a. Find all the extreme points on the flattened sphere with n = 2. What is the distance between the extreme points and the origin?
b. Find all the extreme points on the flattened sphere for integers n > 2. What is the distance between the extreme points and the origin?
c. Give the location of the extreme points in the limit as n → ∞ What is the limiting distance between the extreme points and the origin as n → ∞?
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