Question
Investigate the family of functions $ f(x, y) = e^{cx^2 + y^2} $. How does the shape of the graph depend on $ c $?
Step 1
In this case, the function $f(x, y) = e^{cx^2 + y^2}$ simplifies to $f(x, y) = e^{y^2}$. This is a function of $y$ only, and its graph is a cylindrical surface along the $x$-axis. Show more…
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