6 Hausdorff space in which each point has a compact neighbourhood is locally compact 6 Solve $10x+2x^2+x^3=20$ using only algebra and geometry? 4 Prove that an increasing and surjective function is continuous. 3 If $u(x)=\int_0^x \sin(x-w)w^2 \, dw$, what is $u'$? 3 For odd $m\ge3$, does it follow: $\frac{x^m + y^m}{x+y} + (xy)\frac{x^{m-2} + y^{m-2}}{x+y} = x^{m-1} + y^{m-1}$

### Reputation (731)

 +40 The position of a ladder leaning against a wall and touching a box under it +45 If $u(x)=\int_0^x \sin(x-w)w^2 \, dw$, what is $u'$? +30 Prove that an increasing and surjective function is continuous. +10 Optimization and maximum geometry

### Questions (2)

 21 The position of a ladder leaning against a wall and touching a box under it 2 Peano and consistency, how to understand it rightly.

### Tags (25)

 8 algebra-precalculus × 3 6 general-topology 7 geometry × 3 6 separation-axioms 6 calculus × 3 4 derivatives × 3 6 euclidean-geometry × 2 4 continuity 6 compactness 4 real-analysis

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