query: show that $f''(a)=\lim _{h\to 0}\frac{f(a+h)+f(a-h)-2f(a)}{h^2}$
positive_passages.docid: 119053
positive_passages.text: How to prove that $\displaystyle f''(a)=\lim_{h \to 0}\frac{f(a+2h)-2f(a+h)+f(a)}{h^2}$
negative_passages.docid: 101778
negative_passages.text: Show that there is $\eta\in(0,1)$ with $f''(\eta)=f(\eta)$
negative_passages.docid: 1641
negative_passages.text: Proving $f' = - \frac{\partial{F}/\partial{x}}{\partial{F}/\partial{y}}$
negative_passages.docid: 104263
negative_passages.text: How to show that $f'(x)<2f(x)$
negative_passages.docid: 128218
negative_passages.text: If $\lim \limits_{x \to a}\left(f(x)+\frac{1}{f(x)}\right)=2,$ then $\lim \limits_{x \to a}f(x)=1$
negative_passages.docid: 69008
negative_passages.text: $f'(x) = [f(x)]^{2}$. Prove $f(x) = 0 $
negative_passages.docid: 28399
negative_passages.text: Showing $f$ is constant
negative_passages.docid: 142138
negative_passages.text: Show that $f(x)$ is a constant function if $\lim\limits_{h\to 0}\frac{1}{h^3}\int_{-h}^{h}f(x+t)\cdot t\,dt=0$ for all $x$
negative_passages.docid: 109907
negative_passages.text: How to prove that $\lim\limits_{h \to 0} \frac{a^h - 1}{h} = \ln a$
negative_passages.docid: 34081
negative_passages.text: Prove that $|f''(\xi)|\geqslant\frac{4|f(a)-f(b)|}{(b-a)^2}$
negative_passages.docid: 78538
negative_passages.text: prove $\lim_{n\to\infty}{\frac{a^n}{n!}}=0$
negative_passages.docid: 132431
negative_passages.text: Proving $|f'(z)|\leq\frac{\text{Re}(f(z))}{\text{Re}(z)}$
negative_passages.docid: 64485
negative_passages.text: Proving $\displaystyle\lim_{h\to0}\frac{f(x+h)-2f(x)+f(x-h)}{h^2}=f''(x)$
negative_passages.docid: 142249
negative_passages.text: Show that $\lim_{n\to \infty} \int_E \cos^2(nx + a_n) dx = \frac{1}{2}m(E)$
negative_passages.docid: 78319
negative_passages.text: Show that $x \mapsto \frac{f(x)}{x}$ is strictly increasing on (0,1) given that f '(x) is strictly increasing on (0,1) and that f(0)=0
negative_passages.docid: 109099
negative_passages.text: Prove that $\lim_{h \to 0}\frac{1}{h}\int_0^h{\cos{\frac{1}{t}}dt} = 0$
negative_passages.docid: 13486
negative_passages.text: Show $\lim \limits_{n \to \infty} \frac{a_{n+1}}{a_n} = \|f\|_{\infty}$ for $f \in L^{\infty}$