Answer by Kavi Rama Murthy for Example of function such that its each...
Let $f(x)=\frac 1 {x^{2}}$. Then the conditions are satisfied with $a=2, n=0$. If you insist on an example where $f$ is smooth on the whole line you could multiply this function by a smooth function...
View ArticleAnswer by Rosy for Example of function such that its each derivative and...
$f(x)=\frac{1}{x}$ , then $f^n(x)=\frac{(-1)^n}{x^{n+1}},$ clearly $\lim\limits_{|x|\rightarrow \infty}f^n(x)=0$ for each $n.$Now for each $n$ chose $\alpha>n+1$$\lim\limits_{|x|\rightarrow...
View ArticleExample of function such that its each derivative and itself vanishes at 0...
I wanted to understand defination of schwartz class function .So I am trying to find example of function f(x) such that $\lim_{|x|\to \infty}f^{(n)}(x)=0$ where $n\in \mathbb N\cup\{0\}$ (this should...
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