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math105-s22:hw:hw9

HW 9

  1. Rudin Ex 8.6
  2. Rudin Ex 8.7 (Rudin's $D_i f = \partial f / \partial x_i$)
  3. 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?)
  4. 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