math105-s22:hw:hw9

HW 9

Rudin Ex 8.6
Rudin Ex 8.7 (Rudin's $D_i f = \partial f / \partial x_i$ )
Show that, for any closed subset $E \In \R^2$ , there is a continuous function $f: \R^2 \to \R$ , such that $f^{-1}(0) = E$ . (bonus, can you make $f$ a smooth function?)
For the implicit function theorem, take $n=m=1$ , and interpret it graphically and intuitively.

math105-s22/hw/hw9.txt · Last modified: 2022/03/17 22:16 by pzhou