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### Questions (22)

 4 X is a compact metric space, which of the following must be true? 4 How to evaluate $\int_{0}^{\pi} \log(2+\cos x)dx$? [duplicate] 3 How to prove two topologies $\mathcal{T}_1,\mathcal{T}_2$ are not equal 3 Prove that every irreducible cubic monic polynomial over $\mathbb F_{5}$ has the form $P_{t}(x)=(x-t_{1})(x-t_{2})(x-t_{3})+t_{0}(x-t_{4})(x-t_{5})$? 2 Is this proof about $\pi$ is irrational correct?

### Reputation (308)

 +5 X is a compact metric space, which of the following must be true? +5 What does $e^z,|z|=1$ look like？ +20 How to evaluate $\int_{0}^{\pi} \log(2+\cos x)dx$? +5 How to prove $\lim_{n\to \infty} \prod_{i=0}^{n-1}$ $(2+\cos \frac{i \pi}{n})^{\frac{\pi}{n}}$=$\sqrt{3}$ by the sum form of a integration?

 1 How to calculate $\displaystyle\lim_{x \to \infty} \left ( \frac{x+2}{x} \right )^{x}=e^{2}$ 0 How to find $\lim_{(x,y)\rightarrow (0,0)} \frac{e^{-x^{2}} - y}{x^{2}+y^{2}}$? 0 $5(x + 2) + 2(x-3) < 3(x - 1) + 4x$ leads to nowhere, but why? 0 Why study linear algebra?

### Tags (29)

 1 calculus × 7 0 differential-equations × 2 1 limits × 3 0 integration × 2 0 general-topology × 8 0 polynomials × 2 0 real-analysis × 6 0 irreducible-polynomials 0 abstract-algebra × 4 0 ring-theory

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