7 Determine $\sqrt{1+50\cdot51\cdot52\cdot53}$ without a calculator? 6 Looking for other approaches to evaluate $\lim _{x\to 0^+}\frac{\sin 3x}{\sqrt{1-\cos ^3x}}$ 4 If $\dim(\operatorname{Im}T)=1$ then $T$ is diagonalizable 4 Problem applying L'Hopitals rule. 4 Value of $\sin^{-1}(\sin 10)$

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### Questions (21)

 7 Minimizing the sum of the six distances determined by four points in the plane, if each distance is at least $d$ 3 Show $A^{\mathrm{Card}(GL_2(\mathbb{Z/p\mathbb{Z})})+2}=A^2$ for any $A \in \mathcal{M}_2(\mathbb{Z/p\mathbb{Z}})$ 3 Prove there exists a particular basis of $\mathrm{Ker}(u^2+u+Id)$ 3 Kernel and image of a product of two rectangular matrices 3 Infinite number of square roots of a complex matrix

### Tags (106)

 19 calculus × 13 10 algebra-precalculus × 5 17 real-analysis × 18 7 matrices × 9 13 linear-algebra × 21 7 sequences-and-series × 9 12 limits × 6 7 factoring 11 trigonometry × 5 6 functions × 6

### Bookmarks (1)

 2 Can polynomials with coefficients in [-1, 1] uniformly approximate arbitrarily large constant functions?