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1,215
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 13 If $f,g$ are continuous at $a$, show that $h(x)=\max\{f(x),g(x)\}$ and $k(x)=\min\{f(x),g(x)\}$ are also continuous at $a$ 8 If $a>1$, prove that $\lim_{n \rightarrow \infty } a^n = \infty$ 3 How to prove that $\alpha''(s)$ goes towards the inside of the curve $\alpha(s)$ 3 Is Spivak Cheating? 3 Derivative of an integral? $f(y) = \frac{d}{dy} F(y) = \color{red}{\frac{1}{\sqrt{y}}}\Phi'(\sqrt{y})$

### Reputation (1,215)

 +5 Do the BAC-CAB identity for triple vector product have some intepretation? +20 If $f,g$ are continuous at $a$, show that $h(x)=\max\{f(x),g(x)\}$ and $k(x)=\min\{f(x),g(x)\}$ are also continuous at $a$ -2 Dot Product Intuition +5 Example of an additive but not linear map beetween real topological linear spaces

### Questions (27)

 9 Do the BAC-CAB identity for triple vector product have some intepretation? 7 Example of an increasing, integrable function $f:[0,1]\to\mathbb{R}$ which is discontinuous at all rationals? 6 Definition of the Hamiltonian via Legendre transform. 5 How can this result in Thermodynamics be rigorously proved? 3 Differential of the inversion of Lie group [duplicate]

### Tags (70)

 33 real-analysis × 14 5 linear-algebra × 8 26 calculus × 16 5 differential-equations × 6 12 limits × 7 4 algebra-precalculus × 3 10 derivatives × 7 4 probability × 2 7 analysis × 4 3 differential-geometry × 8

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