query: how to prove the continuity of the Taylor $f^{(n)}(\xi(x))$?
positive_passages.docid: 150770
positive_passages.text: Why is $f^n(\xi(x))$ continuous over $x$?
negative_passages.docid: 4062
negative_passages.text: prove that $f(x)=\log(1+x^2)$ is Uniform continuous with $\epsilon ,\delta$ ...
negative_passages.docid: 15914
negative_passages.text: Prove that any polynomial function is continuous
negative_passages.docid: 97256
negative_passages.text: For $f$ continuous, show $\lim_{n\to\infty} n\int_0^1 f(x)x^n\,dx = f(1).$
negative_passages.docid: 98371
negative_passages.text: Convergence of the $e^x$ Taylor series
negative_passages.docid: 55605
negative_passages.text: If $f_n(x_n) \to f(x)$ whenever $x_n \to x$, show that $f$ is continuous
negative_passages.docid: 155923
negative_passages.text: continuity of $f(x,y)$ in $\mathbb R^2$.
negative_passages.docid: 60521
negative_passages.text: Continuity of a convex function
negative_passages.docid: 42817
negative_passages.text: proving $\lim\limits_{n\to\infty} \int_{0}^{1} f(x^n)dx = f(0)$ when f is continous on [0,1]
negative_passages.docid: 134752
negative_passages.text: Proof (epsilon delta) for the continuity of a function at a point
negative_passages.docid: 145368
negative_passages.text: How to show $f:Y\to X^{+}$ is continuous?
negative_passages.docid: 101701
negative_passages.text: Prove that $\ln x$ is not uniformly continuous on $(0,1]$
negative_passages.docid: 80164
negative_passages.text: Taylor expansion of a function containing QPochhammer[q, q, n]
negative_passages.docid: 124499
negative_passages.text: Where is the error in my proof that all derivatives are continuous?
negative_passages.docid: 116460
negative_passages.text: How to prove this inequality using Taylor approximation?
negative_passages.docid: 46642
negative_passages.text: Continuity of $\sin(x)/x$
negative_passages.docid: 115417
negative_passages.text: Continuity of $L^1$ functions with respect to translation