Which of the following functions belong to $S(R)=\{ f \epsilon C^\infty(R): |x^\alpha| \times |D^\beta f(x)| \leq C_{\alpha, \beta} \}$?
a) $f(x)=\frac{sin(x)}{x}$ b) $f(x)=1-e^{-x^{-2}}$ with $f(x)=1$ at $x=0$ c) $f(x)=x^5e^{-x^2}$ d) $f(x)=x^5e^{-|x|}$
I am not sure how to such the functions above are in $S(R^n)$. I do know that all the functions are $C^\infty(R)$ since sin(x), \frac{1}{x}, $e^x$ functions are in $C^\infty(R)$.