Differences

This shows you the differences between two versions of the page.

--- pow:start [2024/03/12 00:25]
mazur
+++ pow:start [2024/05/07 15:59] (current)
mazur
@@ Line 2: / Line 2: @@
 ====== Problem of the Week ======
 ~~NOTOC~~
-<box 85% round orange|Problem 4 (due Monday, March 25) >
+<box 85% round orange| >
-A function $f:\mathbb R^2\longrightarrow \mathbb R$ has the following properties:
+The problem of the week will return in the Fall 2024 semester. We thank everyone who participated this Spring. For the Summer, we suggest reviewing problems from past semesters and working on the additional problems posted at the bottom of the provided solutions.
-a) the partial derivatives $\displaystyle \frac{\partial f}{\partial x}$ and $\displaystyle \frac{\partial f}{\partial y}$ are continuous on $\mathbb R^2$;
-b) $\displaystyle \left (\frac{\partial f}{\partial x}(x,y)\right)^2+\left (\displaystyle \frac{\partial f}{\partial y}(x,y)\right)^2\leq \frac{\partial f}{\partial x}(x,y)$ for every $(x,y)\in \mathbb R^2$;
-c) $f(x,0)=0$ for all $x\in \mathbb R$.
-Prove that $f(x,y)=0$ for all $(x,y)\in \mathbb R^2$.
 </box>
@@ Line 27: / Line 20: @@
 ===== Previous Problems and Solutions=====
+    * [[pow:Problem7s24|Problem 7]] Solved by Sasha Aksenchuk.
+    * [[pow:Problem6s24|Problem 6]] Solved by Sasha Aksenchuk.
+    * [[pow:Problem5s24|Problem 5]] We did not receive any solutions.
+    * [[pow:Problem4s24|Problem 4]] A solution submitted by Beatrice Antoinette.
     * [[pow:Problem3s24|Problem 3]] Solved by Mithun Padinhare Veettil.