17 Why $(-2)^{2.5}$ isn't equal to $((-2)^{25})^{1/10}$? 8 Can you help me solve this? Please just read the argument. 8 Find function $f(x)$ satisfying $\int_{0}^{\infty} \frac{f(x)}{1+e^{nx}}dx=0$ 7 If $f(x)=f(2x)$, then how do we get the solution $f(x)=\sin ( \log _a (x))$ through computation? 6 How to solve $\ln t = t-1$ to get $t=1$?

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### Questions (4)

 5 Prove that there exists no choice of parameters such that this expression is an integer 3 Prove this sequence of recursively defined sets converges to the natural numbers 2 For $f_n \in C^\infty (\mathbb{R})$, prove $xf_n(x) \to 0$ uniformly given some conditions on all derivatives. 1 Where Does Arzela's Theorem Fail in this Classic Example?

### Tags (72)

 24 calculus × 7 10 functional-analysis × 3 20 algebra-precalculus × 2 10 integration × 3 17 real-analysis × 12 8 elementary-set-theory 17 exponentiation 8 proof-writing 15 analysis × 6 8 proof-explanation

### Bookmarks (6)

 194 Any open subset of $\Bbb R$ is a countable union of disjoint open intervals 158 Open problems in General Relativity 144 How to determine with certainty that a function has no elementary antiderivative? 44 Given a group $G$, how many topological/Lie group structures does $G$ have? 26 A fiber bundle over Euclidean space is trivial.