Stefan
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 10 How does $3^n-1+2 \cdot 3^n$ evaluate to $3^{n+1}-1$? 8 How does $2^{k+1} = 2 \times 2^k$? 8 Proof of invertibility 7 Prove that $H=0$ or $H=\mathbb{Q}$ 6 Suppose that $f$ is a differentiable function such that $f(g(x)) = x$ and $f^\prime(x) = 1+ [f(x)]^2$. Show that $g^\prime(x) = \frac{1}{1+x^2}$.

### Reputation (2,165)

 +75 Suppose that $f$ is a differentiable function such that $f(g(x)) = x$ and $f^\prime(x) = 1+ [f(x)]^2$. Show that $g^\prime(x) = \frac{1}{1+x^2}$. +20 If $\alpha$ and $\beta$ are ordinals then $\alpha \in \beta \Leftrightarrow \alpha \subsetneq \beta$ +10 If $n-1$ is prime show it is relatively prime. +15 Prove that $[(a|b)\land(c|d)]\Longrightarrow ac|bd;\, a|b\Longrightarrow ac|bc;\, ac|bc\Longrightarrow a|b.$

### Questions (2)

 3 Norm of operator $g\mapsto \int fg$ 0 Show that $U \subset V \Leftrightarrow V^\bot \subset U^\bot$ for $U,V$ subspaces in a Hilbertspace

### Tags (66)

 26 linear-algebra × 11 12 derivatives × 3 25 algebra-precalculus × 7 11 sequences-and-series × 6 22 calculus × 11 10 elementary-set-theory × 5 17 real-analysis × 9 10 functions × 4 14 abstract-algebra × 4 8 vector-spaces × 3

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 Custodian × 4 Enlightened Pundit Nice Answer Explainer Analytical Yearling × 2 Enthusiast Civic Duty Citizen Patrol

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