query: Spivak's Calculus 8-8(a)
positive_passages.docid: 157731
positive_passages.text: Show that one-sided limits always exist for a monotone function (on an interval)
negative_passages.docid: 49556
negative_passages.text: Single Variable Calculus Reference Recommendations
negative_passages.docid: 9918
negative_passages.text: Please verify my epsilon - delta proof $\lim_{x\to 2}⁡(x^3 )=8,$ and $0 < x < 4$
negative_passages.docid: 155165
negative_passages.text: Prove that $\mathbb F_8=\mathbb F_2[X]/(X^3+X+1)$
negative_passages.docid: 106284
negative_passages.text: Establishing a Basis for $F[x]/(f(x))$
negative_passages.docid: 68389
negative_passages.text: Proving $ \frac{(a-b)^2}{8a}\leqslant\frac{a+b}{2} - \sqrt{ab} \leqslant\frac{(a-b)^2}{8b}$ when $ 0<b\le a$
negative_passages.docid: 64629
negative_passages.text: Real Analysis Use of Darboux's Theorem Help
negative_passages.docid: 68746
negative_passages.text: What is $f(f^{-1}(A))$?
negative_passages.docid: 86756
negative_passages.text: Can we teach Mathematica about functional differentiation?
negative_passages.docid: 28096
negative_passages.text: Finding the derivative of $x\uparrow\uparrow n$
negative_passages.docid: 28374
negative_passages.text: calculus expressions
negative_passages.docid: 42923
negative_passages.text: A Book for abstract Algebra
negative_passages.docid: 128383
negative_passages.text: Complex Analysis - Bruce P . Palka - Ex: 4.12
negative_passages.docid: 61671
negative_passages.text: Discrete Math: Writing Proofs
negative_passages.docid: 50735
negative_passages.text: The integral $\int_0^8 \sqrt{x^4+4x^2}\,dx$
negative_passages.docid: 112402
negative_passages.text: Series - Apostol Calculus Vol I, Section 10.20 #24
negative_passages.docid: 76892
negative_passages.text: Factoring inequalities on Double Summation (Donald Knuth's Concrete Mathematics)