query: Limits of functions with the property $f(x) \geqslant g(x)$
positive_passages.docid: 144589
positive_passages.text: Proving that if $f(x) \le g(x)$ then $f(x_0) \le g(x_0)$
negative_passages.docid: 127887
negative_passages.text: Existence of a meromorphic functions $f(z)$ such that $|f(z)|\geq |z|$.
negative_passages.docid: 136659
negative_passages.text: Composition of limits
negative_passages.docid: 33486
negative_passages.text: Negation of the Definition of Limit of a Function
negative_passages.docid: 134070
negative_passages.text: $g$ a restriction of a homeomorphic function $f$, $g$ also homeomorphic?
negative_passages.docid: 58178
negative_passages.text: Property of Entire Functions
negative_passages.docid: 103285
negative_passages.text: Limit of a periodic function
negative_passages.docid: 102478
negative_passages.text: $X_n\leq Y_n$ implies $\liminf X_n \leq \liminf Y_n$ and $\limsup X_n \leq \limsup Y_n$
negative_passages.docid: 135999
negative_passages.text: One sided limit of an increasing function defined on an open interval
negative_passages.docid: 64932
negative_passages.text: Show that $\lim_{x\to a^{+}} g(x) =g(a)$
negative_passages.docid: 126256
negative_passages.text: Prove limit of function
negative_passages.docid: 66824
negative_passages.text: Two definitions of $\limsup$
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: 28413
negative_passages.text: Limit of a continuous function
negative_passages.docid: 5419
negative_passages.text: Continuous functions with $f^2(x)=g^2(x)\neq 0$
negative_passages.docid: 142494
negative_passages.text: Functions $f(x)/g(x), g(x)/h(x),h(x)/f(x)$ are constant
negative_passages.docid: 151410
negative_passages.text: Inequality of continuous functions