query: If $\lim_{x\to\infty}f(x)=0$, does $\lim_{x\to\infty}f'(x)=0$ as well?
positive_passages.docid: 24471
positive_passages.text: Does the derivative of a continuous function goes to zero if the function converges to it?
negative_passages.docid: 122485
negative_passages.text: Limit of $f(x+\sqrt x)-f(x)$ as $x \to\infty$ if $|f'(x)|\le 1/x$ for $x>1$
negative_passages.docid: 107795
negative_passages.text: If $\,f''(x) \ge f(x)$, for all $x\in[0,\infty),$ and $\,f(0)=f'(0)=1$, then is $\,f(x)>0$?
negative_passages.docid: 100765
negative_passages.text: If $f'(x) = 0$ for all $x \in \mathbb{Q}$, is $f$ constant?
negative_passages.docid: 49929
negative_passages.text: If $ \lim_{n \to \infty} (2 x_{n + 1} - x_{n}) = x $, then is it true that $ \lim_{n \to \infty} x_{n} = x $?
negative_passages.docid: 46156
negative_passages.text: How to find $\lim_{x \to \infty} [x]/x$?
negative_passages.docid: 58361
negative_passages.text: Is there a continuous function such that $\int_0^{\infty} f(x)dx$ converges, yet $\lim_{x\rightarrow \infty}f(x) \ne 0$?
negative_passages.docid: 149601
negative_passages.text: $\lim_{x\to{\infty}} (x-\sqrt{x^2+x})$
negative_passages.docid: 86409
negative_passages.text: Show that $\lim_{x \to +\infty}\left(f(x)+f'(x)\right)=0 \Rightarrow \lim_{x \to +\infty} f(x)=0$
negative_passages.docid: 29180
negative_passages.text: If $f(x/n)\to0$ when $n\to\infty$, for every $x$ and $f$ is continuous, then $f(x)\to0$ when $x\to0$, or not?
negative_passages.docid: 132738
negative_passages.text: Showing $\lim_{n \to \infty} m(E_n) = 0$, assuming $f > 0$ a.e. and $\lim_{n \to \infty} \int_{E_n}f \,dm =0$
negative_passages.docid: 80060
negative_passages.text: Is $\frac{1}{\infty}$  equal zero?
negative_passages.docid: 91680
negative_passages.text: Does $\lim_{n\to \infty} \int^{\infty}_{-\infty} f_n(x) dx\, = \int^{\infty}_{-\infty} f(x)\,dx\,$?
negative_passages.docid: 143874
negative_passages.text: Limit of derivative is zero. Does it imply a limit for f(x)?
negative_passages.docid: 52632
negative_passages.text: $f\colon(0,\infty)\to \mathbb R$ be continuous ; $f(x)\le f(nx) , \forall n \in \mathbb N , \forall x >0$ , then $\lim_{x\to \infty} f(x)$ exists?
negative_passages.docid: 64169
negative_passages.text: Why isn't $\lim \limits_{x\to\infty}\left(1+\frac{1}{x}\right)^{x}$ equal to $1$?
negative_passages.docid: 129579
negative_passages.text: If $f''(x_0)$ exists then $\lim_{x \to x_0} \frac{f(x_0+h)-2f(x_0)+f(x_0-h)}{h^2} = f''(x_0)$