Episode #125 of the Stack Overflow podcast is here. We talk Tilde Club and mechanical keyboards. Listen now
kryomaxim

 15 How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$? 8 How to derive this formula: $\int_a^bf(c-x)dx = \int_{c-b}^{c-a}f(x)dx$? 5 Can we say that $\det(A+B) = \det(A) + \det(B) +\operatorname{tr}(A) \operatorname{tr}(B) - \operatorname{tr}(AB)$. 4 Integral of root of $\sec x$ 4 What is the way of integrating $\dfrac{-e^x\sin x}{e^x+1}$?

### Reputation (2,378)

 -2 Question about the definition of a semialgebra +5 What are the n-fold derivative of a Legendre transformed quantity? -2 Do commutative matrices share the same eigenvectors? +10 Reference request: Carnot Algebra

### Questions (39)

 11 What is the purpose of K-Theory? 8 Topological invariants by integrals 5 How to show $\int_0^{\infty} \frac{\sin(bx)\sin(x)}{x^2} \prod_{k=1}^n \cos^{p_k}(a_kx) \, \text{d} x= \frac{\pi}{2}$? 5 Manifold is cut along hypersurfaces; how to define a connection on this? 5 How to find the definite integral $\int_0^\infty \frac{x}{\sinh ax}\;dx$

### Tags (172)

 32 calculus × 51 15 proof-explanation 28 integration × 31 13 definite-integrals × 8 21 trigonometry × 7 12 linear-algebra × 19 16 limits × 14 11 matrices × 16 15 limits-without-lhopital 9 ordinary-differential-equations × 17