query: Evaluate the limit with Taylor series
positive_passages.docid: 44668
positive_passages.text: Limit of $x\left(\left(1 + \frac{1}{x}\right)^x - e\right)$ when $x\to\infty$
negative_passages.docid: 56365
negative_passages.text: Evaluate $\sum\limits_{k=1}^{n} \frac{k}{2^k}$
negative_passages.docid: 127001
negative_passages.text: Evaluate $\lim_{x\to \infty} \cos (\sqrt {x+1})-\cos (\sqrt x)$
negative_passages.docid: 113172
negative_passages.text: Please show me how to calculate the folowing limit of a sequence
negative_passages.docid: 47509
negative_passages.text: What are the practical applications of the Taylor Series?
negative_passages.docid: 125497
negative_passages.text: Evaluating $\lim_{n \to \infty} n\left(1-\frac{1}{e}\left(1+\frac{1}{n}\right)^{n} \right)$
negative_passages.docid: 71391
negative_passages.text: Find the limit of given sequence
negative_passages.docid: 126578
negative_passages.text: Evaluate $\lim_{(x,y)\to(0,0)}\frac{\cos(xy)-1}{x^2y^2}$
negative_passages.docid: 3200
negative_passages.text: Limit of integral without Taylor expansion
negative_passages.docid: 107764
negative_passages.text: Limit series $(a^n-b^n)^{1/n}$
negative_passages.docid: 97522
negative_passages.text: Calculating a limit with Harmonic number
negative_passages.docid: 126762
negative_passages.text: taylor series of $\ln(1+x)$?
negative_passages.docid: 115210
negative_passages.text: Evaluate $\lim\limits_{x \to a} \frac{x^m-a^m} {x-a}$
negative_passages.docid: 156546
negative_passages.text: Evaluate the limit $\lim_{n\rightarrow \infty}\frac{1}{\sqrt{n}}\left(1+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+\ldots+\frac{1}{\sqrt{n}}\right)$
negative_passages.docid: 11516
negative_passages.text: Evaluate the limit: $\lim_{(x,y,z)\to(0,0,0)}\frac{xy+yz^2+xz^2}{x^2+y^2+z^4}$
negative_passages.docid: 36849
negative_passages.text: Show convergence of a given series and find the limit.
negative_passages.docid: 156448
negative_passages.text: Evaluate the limit without using the L'Hôpital's rule