query: Calculate this limit without L'Hopital's rule
positive_passages.docid: 147264
positive_passages.text: $ (1 + x)^{1/x} $ when $ x \to \infty$ without L’Hospital’s Rule
negative_passages.docid: 158447
negative_passages.text: Limit as $(x,y)$ approaches $(0,0)$ of $(1+x^2+y^2)^{\frac{1}{x^2+y^2+xy^2}}$
negative_passages.docid: 158591
negative_passages.text: I want to calculate the limit of: $\lim_{x \to 0} \left(\frac{2^x+8^x}{2} \right)^\frac{1}{x} $
negative_passages.docid: 95962
negative_passages.text: proving a theorem from limit using Hopital rule
negative_passages.docid: 100064
negative_passages.text: How to find the limit without L'Hospital?
negative_passages.docid: 26211
negative_passages.text: Computing $\lim_{x \to \infty} x \biggl[ \frac{1}{e} - \left( \frac{x}{x+1} \right)^x \biggr]$
negative_passages.docid: 3200
negative_passages.text: Limit of integral without Taylor expansion
negative_passages.docid: 155979
negative_passages.text: $\lim_{x\to 0} \frac{\sin x - x}{x^2}$ without L'Hospital or Taylor
negative_passages.docid: 113765
negative_passages.text: $\lim_{x\to0} \frac{x-\sin x}{x-\tan x}$ without using L'Hopital
negative_passages.docid: 115367
negative_passages.text: Limits with cubic root without L’Hopital’s Rule: $\lim_{x\to 1}\frac{\sqrt[3]{x}-1}{x-1} $
negative_passages.docid: 17069
negative_passages.text: Limit $\lim_{x\to \infty} \frac{\sqrt{x+1}+\sqrt{x+2}-\sqrt{4x+12}}{\sqrt{x+2}+\sqrt{x}-\sqrt{4x+12}}$
negative_passages.docid: 61242
negative_passages.text: L'Hôpital's rule does not apply?!
negative_passages.docid: 120493
negative_passages.text: L'hopitals rule with limits
negative_passages.docid: 33701
negative_passages.text: Find this limit using L`Hopitals rule
negative_passages.docid: 65213
negative_passages.text: How to find $\lim\limits_{x\to0}\frac{e^x-1-x}{x^2}$ without using l'Hopital's rule nor any series expansion?
negative_passages.docid: 152557
negative_passages.text: Calculate $ \lim\limits_{n \to \infty} \sum\limits_{k=0}^n \frac{2^{k-1}}{a^{2k-1}+1} $
negative_passages.docid: 70742
negative_passages.text: Evaluate $\lim_{x\rightarrow 0} \frac{\sin (6x)}{\sin(2x)}$ without L'Hopital