Differences

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

--- pow:problem4f21 [2021/10/25 02:56] – created mazur
+++ pow:problem4f21 [2021/10/26 04:35] (current) – mazur
@@ Line 1: / Line 1: @@
+<box 80% round orange| Problem 4 (due Monday, October 25)>
+a) Let $x_1,\ldots, x_n$ be real numbers. Prove that
+\[ \sum_{i=1}^n\sum_{j=1}^n \frac{\sin(x_i-x_j)}{x_i-x_j}\geq \sum_{i=1}^n\sum_{j=1}^n \frac{\sin(x_i+x_j)}{x_i+x_j}
+\]
+with the convention that  $\displaystyle \frac{\sin x}{x}=1$ when $x=0$.
+b) Compute $\displaystyle \int_0^1 \sin 2x\sin 5x \ \text{d}x$.
+</box>
+The problem was solved by Ashton Keith. Ashton's solution is similar to our solution. For details
+see the following link {{:pow:2021fproblem4.pdf|Solution}}.