query: Prove that $f(x) = 0$ on the interval $[0,1]$
positive_passages.docid: 71071
positive_passages.text: Nonzero $f \in C([0, 1])$ for which $\int_0^1 f(x)x^n dx = 0$ for all $n$
negative_passages.docid: 12402
negative_passages.text: Showing a function on $[0,1]$ is the zero function
negative_passages.docid: 14759
negative_passages.text: Prove that $ f(z) = 0 $ for all $ z \in \overline{D}(0,1) $.
negative_passages.docid: 149739
negative_passages.text: Prove: $f(t)\leq t+1$
negative_passages.docid: 1444
negative_passages.text: Prove/Show that Limit is equal to 0.
negative_passages.docid: 48314
negative_passages.text: Show that if a function is not negative and its integral is $0$ than the function is $0$
negative_passages.docid: 82567
negative_passages.text: Prove that $ f(x) $ has at least two real roots in $ (0,\pi) $
negative_passages.docid: 69008
negative_passages.text: $f'(x) = [f(x)]^{2}$. Prove $f(x) = 0 $
negative_passages.docid: 76148
negative_passages.text: Show that $\exists c \in \mathbb{R} : f(c) = 0$
negative_passages.docid: 36133
negative_passages.text: Show that $\inf(\frac{1}{n})=0$.
negative_passages.docid: 13852
negative_passages.text: Assume $f$ is a continuous one-to-one function over an interval. Prove that $f$ is strictly monotone
negative_passages.docid: 126259
negative_passages.text: Minimum of a function on an open interval
negative_passages.docid: 131876
negative_passages.text: Show that $\int_{a}^{b}{x^{n}f(x)dx}=0$, then $f=0$
negative_passages.docid: 42853
negative_passages.text: If $f \geq 0$ is continuous and $\int_{a}^{b} f(x) \, dx = 0$, then $f =0$
negative_passages.docid: 113086
negative_passages.text: Prove or disprove that $f(x) = \sin x/x$ is uniformly continuous over the interval $(0,1)$?
negative_passages.docid: 68774
negative_passages.text: Proving that $f(x)$ is less than or equal to $1+\pi/4$
negative_passages.docid: 18261
negative_passages.text: Prove $\int_{a}^{b}{f(x)dx}>0$.