query: Prove Involving Mean Value Theorem for $x \rightarrow a_+$
positive_passages.docid: 1371
positive_passages.text: Prove that $f'(a)=\lim_{x\rightarrow a}f'(x)$.
negative_passages.docid: 106585
negative_passages.text: Show $d_{1}(x_{n},x)\rightarrow{0}$ if and only if $d_{2}(x_{n},x)\rightarrow{0}$.
negative_passages.docid: 37192
negative_passages.text: proof of the second generalized mean value theorem for integrals
negative_passages.docid: 78599
negative_passages.text: How to prove that $\frac{b-a}{\sqrt{1-a^2}}<\sin^{-1}b-\sin^{-1}a<\frac{b-a}{\sqrt{1-b^2}}$ by using Mean Value Theorem?
negative_passages.docid: 67738
negative_passages.text: Mean Value theorem problem?(inequality)
negative_passages.docid: 116027
negative_passages.text: Is inverse use of mean value theorem right?
negative_passages.docid: 82591
negative_passages.text: Prove $(x+r_1) \cdots (x+r_n) \geq (x+(r_1 \cdots r_n)^{1/n})^{n}$.
negative_passages.docid: 8007
negative_passages.text: Proof of Young's inequality
negative_passages.docid: 74258
negative_passages.text: Show that $(1+\frac{x}{n})^n \rightarrow e^x$ uniformly on any bounded interval of the real line.
negative_passages.docid: 15262
negative_passages.text: Prove $\exists \xi, \eta \in (0,1)$, such that $f(\xi)+f'(\eta)=\xi+\eta$.
negative_passages.docid: 97558
negative_passages.text: Prove that $\left| f'(x)\right| \leq \sqrt{2AC}$ using integration
negative_passages.docid: 56127
negative_passages.text: Prove a function is constant under certain conditions
negative_passages.docid: 77645
negative_passages.text: Generalized mean value theorem
negative_passages.docid: 144601
negative_passages.text: Given $f(x+T) = f(x) + a$, prove that $f(x) = \varphi(x) + {a \over T}x$, where $\varphi(x)$ is periodic with period $T$
negative_passages.docid: 54513
negative_passages.text: Prove $\frac 1{x+1}<\ln\left(\frac{x+1}x\right)<0.5\left(\frac 1x+\frac 1{x+1}\right)$
negative_passages.docid: 67853
negative_passages.text: Prove existence of $\lim_{(x,y) \rightarrow (0,2)} \frac{x (y-2)^3}{3x - 5(y-2)^4}$
negative_passages.docid: 35236
negative_passages.text: Proof $p \vdash q \Rightarrow p$