0
$\begingroup$

For each of the following functions, state whether it is even or odd or periodic. If periodic, what is its smallest period?

  1. $\sin ax \quad (a>0)$
  2. $e^{ax} \quad (a>0)$
  3. $x^m \quad (m= \text{ integer})$
  4. $\tan x^2$
  5. $|\sin (x/b)| \quad (b>0)$
  6. $x\cos ax \quad (a>0)$
  • 1
    What are your thoughts? What did you try? Can you answer at least some of the questions for some of the functions?2012-10-26
  • 0
    well for the first one, it is periodic since sin is periodic function, Likewise (5) is also. The rest are not. I am really stuck on the periodicity2012-10-26
  • 0
    That's correct: do you mean you can't prove your last comment and need hints on that? Or are you stuck on figuring out the smallest periods of (1) and (5)? Seeing if the functions are even or odd should be relatively easy: see if $f(-x) = f(x)$ or $f(-x) = -f(x)$. The first case is even and the second case is odd.2012-10-26
  • 0
    It makes sense. Can you answer the question? I have some ideas, but they will be lacking some nice detail that I want to make sure I have.2012-10-26

1 Answers 1