1617-257/Homework Assignment 10 Solutions

Doing

Solve all the problems in section 15, but submit only your solutions of problems 1, 3, and 6. In addition, solve and submit your solution of the following problem:

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 $\lim _{N\to \infty }\int _{0}^{N}f(x)dx$ does exist (yet do not attempt to compute it).
3. The extended integral $\int _{(0,\infty )}f$ does not exist.

Student Solutions

Student 1