# i.a.m

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Classes will dull your mind, destroy the potential for authentic creativity.
-John Nash

 6 Factoring $3x^2 - 10x + 5$ 5 How to show if $|a_{n+1} - a_{n}| \le \frac{1}{2^n}$ then the sequence is Cauchy. 5 Use L'Hopital's rule to evaluate $\lim_{x \to 0} \frac{9x(\cos4x-1)}{\sin8x-8x}$ 5 How can I approach solving this integral when it appears that u-substitution doesn't work? 4 If $P(x)$ is a polynomial then $\lim_{x \to \infty }P(x) = 0 \iff P(x)=0$,

# 1,247 Reputation

 +10 prove that $a \equiv b \mod m$ is an equivalence relation on the integers +5 Krull dimension in polynomial rings +10 Factoring $3x^2 - 10x + 5$ +10 calculate $\lim_{x \rightarrow 0}\left ( x^{-6}\cdot (1-\cos(x)^{\sin(x)})^2 \right )$

# 30 Questions

 6 Cube root in $C^{*}$-algebra. 5 Spectral radius in Banach Algebra 4 $\lambda-z-e^{-z}=0$ has one solution in the right half plane 4 States and positive elements in $C^*$-algebras 4 Artinian rings and associated prime ideals

# 55 Tags

 14 calculus × 8 8 linear-algebra × 5 13 limits × 8 6 analysis × 7 13 real-analysis × 6 6 algebra-precalculus 12 integration × 5 5 abstract-algebra × 10 9 proof-writing × 6 5 sequences-and-series × 4

# 1 Account

 Mathematics 1,247 rep 218