107 Why do both sine and cosine exist? 78 Is there a bijective map from $(0,1)$ to $\mathbb{R}$? 69 Why there is no sign of logic symbols in mathematical texts? 69 Difference between continuity and uniform continuity 40 Notation for partial derivatives

### Reputation (33,240)

 +10 Why do both sine and cosine exist? +10 Sum from $0$ to $n$ of $n \choose i$? +10 Derivative of the squared $L^2$ norm of a vector function +10 Elliptic Regularity for solutions in distributional sense

### Questions (27)

 11 Short and elegant introduction to Sobolev spaces 11 A limit with integral 8 Proof of the extreme value theorem without using subsequences 7 Integrable monotonic functions 6 Smoothness of a non-local functional

### Tags (197)

 672 calculus × 307 178 trigonometry × 20 645 real-analysis × 279 164 functional-analysis × 65 280 limits × 148 151 analysis × 68 256 integration × 90 123 multivariable-calculus × 81 192 derivatives × 106 121 notation × 33

### Bookmarks (13)

 13 A guess related to Lebesgue differentiation theorem 9 Find $\lim_{n\to\infty}\left(2n\int_{0}^{1}\frac{x^n}{1+x^2}dx\right)^n$ 7 If $\sup_n\int_E f_n(x)\ \mathsf dx\leq M\mu(E)$ then the measure of $\{x\in [0,\infty)\mid f(x)>M\}=0$. 7 Positivity of a convolution integral 5 Show that $h(x)=\max \{f(x,y) : y \in [0,1] \}$ is continuous