Math 211 Tuesday Week 1

Tangent plane example (scroll down for tangent line example)

Parametrize the tangent plane for the parametrized surface \[ \begin{align*} f\colon\mathbb{R}^2&\to\mathbb{R}^3\\ (x,y)&\mapsto(x+y^2,y+x^2,xy) \end{align*} \] at the point $p=(1,1)$.

Feel free to play with the code (click on Evaluate to execute changes). Reloading the page will bring back the original code. Apologies in advance for any Java problems.

Tangent line example

Parametrize the tangent line for the parametrized curve \[ \begin{align*} c\colon\mathbb{R}^1&\to\mathbb{R}^3\\ t&\mapsto(\cos(t),\sin(t),t) \end{align*} \] at the point $t=\pi$.