### Answers (1,984)

 54 Why does simplifying a function give it another limit 34 How to calculate $\lim_{x \to 0} \frac{x^{6000} - (\sin x)^{6000}}{x^2(\sin x)^{6000}}$? 29 Ramanujan's approximation for $\pi$ 26 Motivation for/history of Jacobi's triple product identity 24 Infinite Integration by Parts

### Reputation (52,075)

 +10 Addition formula for elliptic integral of second kind +5 Taylor's Theorem with Peano's Form of Remainder +10 Evaluation of $\lim_{x\rightarrow \infty}\frac{\ln (x)}{x}$ using Squeeze theorem +10 monotonic function can only have simple discontinuity

### Questions (105)

 59 Denesting radicals like $\sqrt{\sqrt{2} - 1}$ 46 Simplest way to get the lower bound $\pi > 3.14$ 39 An infinite series plus a continued fraction by Ramanujan 29 A limit problem $\lim\limits_{x \to 0}\frac{x\sin(\sin x) - \sin^{2}x}{x^{6}}$ 24 What is the use of hyperreal numbers?

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