Show That the Surface Areas for the Functions $f ( x , y ) = 2 x ^ { 2 } + 2 y ^ { 2 }$

question 263

Essay

Show that the surface areas for the functions $f ( x , y ) = 2 x ^ { 2 } + 2 y ^ { 2 }$ and $g ( x , y ) = 4 x y$ over the disk $D = \left\{ ( x , y ) \mid x ^ { 2 } + y ^ { 2 } \leq 1 \right\}$ are equal.

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Definitions:

Nutrients

Substances needed by organisms to live, grow, and reproduce, commonly found in food and essential for maintaining health and vitality.

Anorexia Nervosa

An eating disorder characterized by self-starvation. Affected individuals voluntarily undereat and often overexercise, depriving their vital organs of nutrition. Anorexia can be fatal.

BMI (Body Mass Index)

A numerical calculation that compares a person's weight and height to classify their body mass as underweight, normal weight, overweight, or obese.

Eating Disorders

Mental health disorders characterized by abnormal or disturbed eating habits, which negatively affect a person's health and well-being.