Paramanand Singh

 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 $\pi$ 25 Motivation for/history of Jacobi's triple product identity 24 Infinite Integration by Parts

### Reputation (51,685)

 +10 Why is a repeating decimal a rational number? +10 Scary looking limit with an elegant answer +10 Very indeterminate form: $\lim_{x \to \infty} \left(\sqrt{x^2+2x+3} -\sqrt{x^2+3}\right)^x \longrightarrow (\infty-\infty)^{\infty}$ +10 Limit as $x \to 0$ of $\big(x \int_x^1{\frac{f(t)}{\sin^2(t)}}\: dt\big)$

### Questions (105)

 58 Denesting radicals like $\sqrt[3]{\sqrt[3]{2} - 1}$ 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?

### Tags (224)

 2k calculus × 1071 345 derivatives × 173 2k limits × 886 237 limits-without-lhopital × 156 1k real-analysis × 755 199 analysis × 122 527 sequences-and-series × 224 134 trigonometry × 71 396 integration × 172 128 definite-integrals × 67

### Accounts (13)

 Mathematics 51,685 rep 560171 MathOverflow 594 rep 316 Stack Overflow 128 rep 26 TeX - LaTeX 111 rep 4 Computer Science 101 rep 2