Intereting Posts

Relation of cubic B-splines with cubic splines
Representing a number as a sum of k pth powers
Calculate intersection of vector subspace by using gauss-algorithm
How to motivate the axioms for the inner product
Are there any elegant methods to classify of the Gaussian primes?
Proof of bound on $\int t\,f(t)\ dt$ given well-behaved $f$
Convergence of a compound sequence
Prove that there exist a branch
integrate $\int_{\frac{\pi}{4}}^{\frac{\pi}{2}}{\ln{(\ln{\tan{x}})}dx} $
Number of integer solutions of $x^2 + y^2 = k$
Is there a “one-line” proof of $x<y\Rightarrow x^n<y^n$ (for $n$ an odd natural number)?
Proving bipartition in a connected planar graph
My incorrect approach solving this limit. What am I missing?
What is the difference between independent and mutually exclusive events?
Flat algebras and tensor product

Let $u\in \mathcal{C}^1[a,b]$ be such that $u(a)=u(b)=0$. Show that

$$\int_a^b u^2(x)dx\leq (b-a)^2\int_a^b (u')^2(x)dx$$

using the Schwarz’s inequality.

- Derivative at $0$ of $\int_0^x \sin \frac{1}{t} dt$
- How to do contour integral on a REAL function?
- Are Exponential and Trigonometric Functions the Only Non-Trivial Solutions to $F'(x)=F(x+a)$?
- Examples of statements that are true for real analytic functions but false for smooth functions
- Lebesgue integral question concerning orders of limit and integration
- under what conditions can orthogonal vector fields make curvilinear coordinate system?

- Limit of sequence of sets - Some paradoxical facts
- Why is the graph of a continuous function to a Hausdorff space closed?
- Show that $\lim_{n \rightarrow \infty} \frac{\sin^{n}(\frac{x}{\sqrt{n}})}{\left(\frac{x}{\sqrt{n}} \right)^n} = e^{-\frac{x^2}{6}} $
- Maximum volume change for two sets with small Hausdorff metric in bounded part of $\mathbb{R}^n$
- Relationship between rate of convergence and order of convergence
- If $f(x + y) = f(x) + f(y)$ showing that $f(cx) = cf(x)$ holds for rational $c$
- Show that $f(x) = 0$ for all $x \in $ given $|f'(x)| \leq C|f(x)| $
- Metric spaces problem
- Evaluate $ \int_0^\pi \left( \frac{2 + 2\cos (x) - \cos((k-1)x) - 2\cos (kx) - \cos((k+1)x)}{1-\cos (2x)}\right) \mathrm{d}x $
- Intersection of a properly nested sequence of convex sets , if nonempty and bounded , can never be open?

We have $|u(x)|\leq \int_a^x|u'(t)|dt\leq \sqrt{x-a}\sqrt{\int_a^b|u'(t)|^2}dt$ so

$$u(x)^2\leq (x-a)\int_a^bu'(t)^2dt$$ and integrating

$$\int_a^bu(x)^2dx\leq \frac{(b-a)^2}2\int_a^bu'(t)^2dt.$$

- Prove that the additive group $ℚ$ is not isomorphic with the multiplicative group $ℚ^*$.
- Harmonic number inequality
- Consider the “infinite broom”
- Characterizations of the $p$-Prüfer group
- Prove that $x = 2$ is the unique solution to $3^x + 4^x = 5^x$ where $x \in \mathbb{R}$
- Is the class of subsets of integers countably infinite?
- Everywhere Super Dense Subset of $\mathbb{R}$
- Can a non-periodic function have a Fourier series?
- improper integral convergence test
- Simple question on conditional probabilities (multidimensional normal distributions)
- A linear system of a curve on a K3 surface.
- Does $a^3 + 2b^3 + 4c^3 = 6abc$ have solutions in $\mathbb{Q}$
- Using tan(x), show that open interval is diffeomorphic with the real line
- About the Polya-Knopp-like inequality $\sum_{k=1}^{n}\frac{k^2}{a^2_{1}+\cdots+a^2_{k}}\le\left(\frac{1}{a_{1}}+\cdots+\frac{1}{a_{n}}\right)^2$
- $\int_{-2}^{2} \sin(x^5)e^{(x^8\sin(x^4))} dx$