kaiserphellos

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12 Questions

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8	Prove that $\lim\limits_{n\rightarrow \infty}\int_1^3\frac{nx^{99}+5}{x^3+nx^{66}} d x$ exists and evaluate it.
4	Commutative ring $R$ such that $R[x]$ has nonconstant units.
3	Help with series indices in proving the associativity of multiplication of formal power series
3	Exercise on Limits of Functions
2	If $0\neq \alpha \in E$ is algebraic over F, then $\frac{1}{a}$ is also algebraic over F.

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170 Reputation

+10	If $0\neq \alpha \in E$ is algebraic over F, then $\frac{1}{a}$ is also algebraic over F.
+10	Prove that $\|\sum_{k=1}^\infty(1-\cos(1/k))\|\leq 2$.
+5	Show that $f(x)=\sum_{k=1}^\infty \frac{1}{k}\sin(\frac{x}{k+1})$ converges.
+5	Prove that $\lim\limits_{n\rightarrow \infty}\int_1^3\frac{nx^{99}+5}{x^3+nx^{66}} d x$ exists and evaluate it.

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0 real-analysis × 9	0 extension-field
0 homework × 9	0 limit
0 abstract-algebra × 3	0 analysis
0 sequences-and-series × 2	0 optimization
0 convergence	0 convex-analysis

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