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 32 How to calculate $z^4 + \frac1{z^4}$ if $z^2 + z + 1 = 0$? 27 Example of an infinite sequence of irrational numbers converging to a rational number? 20 Determinant of a specially structured matrix ($a$'s on the diagonal, all other entries equal to $b$) 17 General Lebesgue Dominated Convergence Theorem 15 Prove: $\binom{n}{k}^{-1}=(n+1)\int_{0}^{1}x^{k}(1-x)^{n-k}dx$ for $0 \leq k \leq n$

### Reputation (13,997)

 +10 Prove $\cos(n)$ does not converge as $n$ tends to infinity +5 sum of concave and convex function +10 $\lim f(x) = L, \lim g(x) = M\implies \lim \max\{f(x),g(x)\} = \max\{L,M\}$ +15 Metric Matrix of the hyperbolic Riemannian manifold

### Questions (12)

 7 Is the following integral positive? 6 Prove that an integral is positive 4 calculation of normal derivative 4 Boundary of the boundary of a manifold is empty 4 Is the derivative of this function bounded?

### Tags (143)

 186 calculus × 64 73 complex-analysis × 25 145 differential-geometry × 51 66 matrices × 22 116 real-analysis × 30 63 sequences-and-series × 14 103 linear-algebra × 36 61 graph-theory × 14 88 integration × 29 59 algebra-precalculus × 10

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