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

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 $\mathbb { R } ^ { 3 }$ .