query: Why does $\frac{\sin x}{x}$ have no anti-derivative
positive_passages.docid: 28441
positive_passages.text: Why can't the indefinite integral $\int\frac{\sin(x)}{x}\mathrm dx$ be found?
negative_passages.docid: 125088
negative_passages.text: show that $ \lim(\sin(\frac{1}{x}))$ as $x$ approaches zero does not exist.
negative_passages.docid: 101546
negative_passages.text: Lebesgue integral $\int_{(0, \infty)} \frac{\sin x}{x} dm$ doesn't exist but improper Riemann integral exists
negative_passages.docid: 27969
negative_passages.text: Why does $\frac{1}{x} < 4$ have two answers?
negative_passages.docid: 27888
negative_passages.text: Why is $|x|$ not differentiable at $x=0$?
negative_passages.docid: 16642
negative_passages.text: Showing $a_n=\sin(n)$ does not converge
negative_passages.docid: 19561
negative_passages.text: Why is $\frac{1}{\frac{1}{X}}=X$?
negative_passages.docid: 80710
negative_passages.text: Does $\int_{-1}^1 \frac 1 x dx$ equal zero?
negative_passages.docid: 19828
negative_passages.text: Show that $\frac{x^3}{x^2+y^2}$ is not differentiable at $(0,0)$, even though all directional derivatives exist
negative_passages.docid: 97213
negative_passages.text: Why does $\sin(0)$ exist?
negative_passages.docid: 13533
negative_passages.text: Proof that the limit of $\frac{1}{x}$ as $x$ approaches $0$ does not exist
negative_passages.docid: 885
negative_passages.text: Why is the 2nd derivative written as $\frac{\mathrm d^2y}{\mathrm dx^2}$?
negative_passages.docid: 129394
negative_passages.text: understanding $\frac{\partial x}{\partial y}\frac{\partial y}{\partial z}\frac{\partial z}{\partial x}=-1$
negative_passages.docid: 59911
negative_passages.text: Looking for help with a proof that n-th derivative of $e^\frac{-1}{x^2} = 0$ for $x=0$.
negative_passages.docid: 18201
negative_passages.text: Why isn't the derivative of $e^x$ equal to $xe^{(x-1)}$?
negative_passages.docid: 150734
negative_passages.text: Solving $\lim\limits_{x\to0} \frac{x - \sin(x)}{x^2}$ without L'Hospital's Rule.
negative_passages.docid: 87743
negative_passages.text: Is a function whose derivative vanishes at rationals constant?