Convergence of a sequence of a continuously differentiable function

Asked Sep 08 '17 at 16:08

Active Sep 08 '17 at 16:10

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Let $f(x): \mathbb{C}^M \rightarrow R$ be a continuously differentiable function of complex vector $x$. Besides, let us assume that $\{x_n\}$ is a sequence of $x$. If we know that sequence $\{f(x_n)\}$ converges to a value (less than $\infty$), can we claim that $\{x_n\}$ also converges?

Note: we also know that $\{f(x_n)\}$ is increasing and bounded from the top.

edited Sep 08 '17 at 16:10

asked Sep 08 '17 at 16:08

Shahram Shahsavari

1

$f$ could be a constant function... – orangeskid Sep 08 '17 at 16:10
We know that it is not a constant function – Shahram Shahsavari Sep 08 '17 at 16:12
4

$x_n= (1-1/n, n)$, $f(a,b)=a$ – orangeskid Sep 08 '17 at 16:14

Convergence of a sequence of a continuously differentiable function

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