query: How to show that $f(A)$ is an open interval.
positive_passages.docid: 142740
positive_passages.text: If $\varphi \in E'$ and $A$ is convex and open then $\varphi (A)$ is an open interval
negative_passages.docid: 41037
negative_passages.text: Prove that $f'(a)=\lim_{n\to\infty}\frac{f(b_n)-f(a_n)}{b_n-a_n}$ under some conditions
negative_passages.docid: 105084
negative_passages.text: Let f be a function twice differentiable and with derivatives continuous on an interval $[a,b]$ containing $0$. Prove the following statement:
negative_passages.docid: 69283
negative_passages.text: The limit points of an open interval (open set)
negative_passages.docid: 21879
negative_passages.text: Show that if $\lim_{x\to a}f'(x) = A$ then $f'(a)$ exists and equals A
negative_passages.docid: 61500
negative_passages.text: If f is continous and exist real numbers show that $f(x)=0$
negative_passages.docid: 125233
negative_passages.text: Why is an open interval not a compact set?
negative_passages.docid: 106843
negative_passages.text: Give an example where $\int_{\bar A} f$ exists but $\int_A f$ does not for a continuos $f$ on a bounded open subset $A$ of $\mathbb{R}^n $
negative_passages.docid: 53627
negative_passages.text: Proving continuity of $f$
negative_passages.docid: 115636
negative_passages.text: Show that $f$ is either injective or a constant function.
negative_passages.docid: 39692
negative_passages.text: The length of an interval covered by an infinite family of open intervals
negative_passages.docid: 4636
negative_passages.text: How to show that $f$ is differentiable at $x=0.$
negative_passages.docid: 153934
negative_passages.text: How to prove that a set R\Z is open
negative_passages.docid: 66691
negative_passages.text: Real function continuous on closed interval implies it is bounded - over-simple proof??
negative_passages.docid: 99236
negative_passages.text: Interior of closure of an open set
negative_passages.docid: 80421
negative_passages.text: Show that $a - b \mid f(a) - f(b)$
negative_passages.docid: 153730
negative_passages.text: Show that $f(x)=x^2$ is continuous at $a=2$ using the $\delta-\epsilon$ definition of continuity.