Prove that the lines $v=k\pi$ are asymptotic lines for the surface parametrized by $$\varphi:(0,\pi )\times\mathbb{R}\rightarrow\mathbb{R}^{3}$$ $$\varphi (u,v)=(v,\cos(u),\sin(v))$$
Honestly, I don't know how to proceed because the professor talk with us only about the $v$ or $u-lines$ like $\varphi (u_{0}+t,v)$, $t\in\mathbb{R}$
Can someone axplain this concept? Thanks before!
According to your description, we can plot the function using Mathematica:
I do not think it have any "asymptotic lines".