sj134

### Questions (60)

 7 Prove $\frac{c_n(a_1,\ldots,a_n)}{c_{n-1}(a_2,\ldots,a_n)}=a_1 + \frac{1}{a_2 + \frac{1}{\ddots + \frac{1}{a_{n-1}+\frac{1}{a_n}}}}$ 6 Show there exists $g:(0,1)\to\mathbb{R}^2$ such that $h\circ g$ constant, $g$ continuously differentiable and $g$ injective 4 Show $\exists x$ such that $Df(x) = 0$ for $f = 0$ 4 Show isomorphism $W_1 \hookrightarrow V \twoheadrightarrow W_2$ 3 Splitting field of $X^6-7X^4+3X^2+3$ over $\mathbb Q$ and $\mathbb F_{13}$

### Reputation (307)

 +5 Proof rearranged alternating harmonic series tends to $\frac{3s}2$ +5 Prove $\frac{c_n(a_1,\ldots,a_n)}{c_{n-1}(a_2,\ldots,a_n)}=a_1 + \frac{1}{a_2 + \frac{1}{\ddots + \frac{1}{a_{n-1}+\frac{1}{a_n}}}}$ +5 Splitting fields of $(X^3-2)(X^2-2)$ +10 Show $f$ locally invertible with continuously differentiable inverse function, but $\#f^{-1}(\{z\}) = 2$

### Tags (43)

 4 real-analysis × 15 0 bilinear-form × 5 0 linear-algebra × 26 0 polynomials × 4 0 abstract-algebra × 10 0 splitting-field × 4 0 galois-theory × 5 0 analysis × 3 0 sequences-and-series × 5 0 convergence × 3