Decaf-Math

 33 Efficiently evaluating $\int x^{4}e^{-x}dx$ 11 Are there any irrational numbers that have a difference of a rational number? 5 Let $f(x)= 2x^3 +Ax^2 +4x -5$; find $A$ given $f(2) =5$ 5 Do these points make a straight line? 5 Integral Problem: $\int_{0}^{1} \sqrt{e^{2x}+e^{-2x}+2}$

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### Questions (98)

 6 Show $\pmatrix{A & B\\ C & I}$ is nonsingular given that $A-BC$ is nonsingular. 6 Let $P \in M_n(\mathbb C)$ be idempotent. Prove that all nonzero singular values of $P$ satisfy $\sigma_i \ge 1$ 5 Compute $\lim_{x\to0}{1 - e^{-x}\over e^x - 1}$ 5 Transversals of Latin Squares 5 Proof that the Period of $\sin(x)$ is $2\pi$.

### Tags (143)

 70 calculus × 32 11 irrational-numbers 58 integration × 17 11 number-theory 22 algebra-precalculus × 26 11 rationality-testing 17 linear-algebra × 38 8 real-analysis × 36 13 transcendental-numbers × 2 8 limits × 13

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