query: continuity of $\sqrt{x}$ at $x=0$
positive_passages.docid: 141945
positive_passages.text: Why is $f(x) = \sqrt{x}$ is continuous at $x=0$? Does $\lim_{x \to 0^{-}} \sqrt{x}$ exist?
negative_passages.docid: 157847
negative_passages.text: If $x_n \to 0$, show that $\sqrt{x_n} \to 0$
negative_passages.docid: 59519
negative_passages.text: What about the continuity of these functions in the uniform topology?
negative_passages.docid: 61472
negative_passages.text: If $0<x<y$, then prove that $\sqrt{x} <\sqrt{y}$ and $x <\sqrt{xy} <y$
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: 154572
negative_passages.text: Continuity of a function at an isolated point
negative_passages.docid: 110146
negative_passages.text: I need to prove the continuity of $f(x)=\log x$ using a $\epsilon-\delta$ proof
negative_passages.docid: 60521
negative_passages.text: Continuity of a convex function
negative_passages.docid: 111990
negative_passages.text: Continuous function from $(0, 1]$ onto $(0, 1)$?
negative_passages.docid: 145368
negative_passages.text: How to show $f:Y\to X^{+}$ is continuous?
negative_passages.docid: 81223
negative_passages.text: Real Analysis Question: continuity of $f(x) = \sum_{q_n<x} 1/n^2$
negative_passages.docid: 58664
negative_passages.text: Proving a function is continuous for a fixed variable
negative_passages.docid: 84785
negative_passages.text: Is $f(x)=x+\frac{x}{x+1}$ uniformly continuous on $(0,\infty)$
negative_passages.docid: 126227
negative_passages.text: continuity of a probability measure if $\mu (\{x\})=0$
negative_passages.docid: 8836
negative_passages.text: If $f$ is continuous on $[a , b]$ and $\int_a^b f(x) p(x)dx = 0$ then $f = 0$
negative_passages.docid: 115077
negative_passages.text: Prove continuity for cubic root using epsilon-delta
negative_passages.docid: 44574
negative_passages.text: Continuity of absolute value of a function