# 1617-257/Homework Assignment 10 Solutions

Problem A. Consider the function $f\colon[0,\infty)\to{\mathbb R}$ defined by $f(x)=\sin(x^2)$. Show that
1. The limit $\lim_{x\to\infty}f(x)$ does not exist.
2. The limit $\lim_{N\to\infty}\int_0^Nf(x)dx$ does exist (yet do not attempt to compute it).
3. The extended integral $\int_{(0,\infty)}f$ does not exist.