Question

Explain why the function $z=g(x,y)=f\left(\sqrt{x^2+y^2}\right)$is the equation of the surface obtained when the graph of $f$ is rotated about the $z$-axis. Sketch the surface obtained when your function from Exercise 13 is rotated about the $z$-axis.

Short answer

The function $z=g(x,y)=f\left(\sqrt{x^2+y^2}\right)$is associated with two variable $x$ and $y$. When the function is rotated about $z$ - axis, a surface is generated in two variables $x$ and $y$.

Step-by-step solution

Given Information and Calculation

The objective of this problem is to explain why the function$z=g(x,y)=f\left(\sqrt{x^2+y^2}\right)$is equation of the surface obtained of $f$is rotated about the $z$-axis.

The function $z=g(x,y)=f\left(\sqrt{x^2+y^2}\right)$is associated with two variable$x$and $y$. When the function is rotated about $z$- axis, a surface is generated in two variables $x$and $y$.