1617-257/Homework Assignment 10 Solutions

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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^Nf(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

Student 2