Tagged Questions
0
votes
1answer
38 views
Can we deduce that $\lim_{x\to+\infty}f(x)=\pm\infty$ or $\lim_{x\to-\infty}f(x)=\pm\infty$?
Let $f:ℝ→ℝ$ be rael analtic function. Asume that $f$ is of finite order $1$ (An entire function is said to be of finite order if there exist numbers $a,r>0$ such that
$$|f(x)|≤exp(|x|^{a})$$ for ...
1
vote
1answer
56 views
Behavior at infinity.
Classify the behavior at $\infty$ for $$f(z)=\frac{\sin z}{z^2},\,g(z)=\frac{1}{\sin z},\,h(z)=\exp\left(\tan\frac{1}{z}\right).$$
So I just considered $f(1/z),g(1/z),h(1/z)$ at $z=0$. For $f$ I ...
5
votes
2answers
91 views
$\lim_{x\rightarrow\infty}\frac{f(x)}{e^x}$ for analytic functions
For some analytic function $f(x)=\lim_{n\rightarrow\infty}\sum^n_{r=0}c_rx^r$,
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