Let $f ( x , y ) = x ^ { 2 } + y ^ { 2 }$

question 38

Essay

Let $f ( x , y ) = x ^ { 2 } + y ^ { 2 }$ .(a) Sketch the intersection of $z = f ( x , y )$ and $z = 1$ in the $x y$ -plane.(b) Sketch the intersection of $z = f ( x , y )$ and $x = 1$ in the $x y$ -plane.(c) Sketch the intersection of $z = f ( x , y )$ and $y = 1$ in the $x y$ -plane.(d) Sketch the graph of $z = f ( x , y )$ in $\mathbb { R } ^ { 3 }$ .

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Definitions:

Olfaction

The sense of smell, a chemical sense that detects odors or scents through sensory organs in the nose.

Alveolar Process

Part of the jawbone that contains the sockets (alveoli) for teeth.

Crista Galli

A vertical projection of the ethmoid bone in the skull, serving as the point of attachment for membranes dividing the nasal cavity.

Supraorbital Foramen

An opening or notch in the frontal bone of the skull, above the eye orbit, through which the supraorbital nerve and vessels pass.