Intereting Posts

Help on the relationship of a basis and a dual basis
A function for which one-sided limits are zero and infinity
Sum of $\Gamma(n+a) / \Gamma(n+b)$
What is $\lim_{x\to\infty}\left(\sin{\frac 1x}+\cos{\frac 1x}\right)^x$?
Generate a random direction within a cone
Limit Definition when Right-Hand Limit has Nonempty Domain but Left-Hand Limit has Empty Domain
Proof of recursive formula for “fusible numbers”
Rank of the $n \times n$ matrix with ones on the main diagonal and $a$ off the main diagonal
4 points in 3-d space (one known and three unknown)
Archimedean Property and Real Numbers
Spherical coordinates for sphere with centre $\neq 0$
How do I calculate $\lim_{x\to+\infty}\sqrt{x+a}-\sqrt{x}$?
Curve enclosing the maximum area
Geometric visualization of covector?
Number of solutions for $x + x + \ldots + x =k$

Given:

$0 \le a \le 1$

$0 \le b \le 1$

- Proving $\sqrt{x + y} \le \sqrt{x} + \sqrt{y}$
- Rationalizing radicals
- Gaussian proof for the sum of squares?
- Prove that $\frac{a^2}{a + b} + \frac{b^2}{b + c} + \frac{c^2}{c + a} \ge \frac{3}{2}$
- Integer values of $\frac{x}{y}+\frac{y}{z}+\frac{z}{x}$?
- Proportional to 2 Separate Variables vs. Proportional to Product of 2 Variables

Prove: $a + b – ab \le 1$

- Prove $0! = 1$ from first principles
- Show that $|z_1 + z_2|^2 < (1+C)|z_1|^2 + \left(1 + \frac{1}{C}\right) |z_2|^2$
- Prove by contradiction or contrapositive? If $|x+y|<|x|+|y|$, then $x<0$ or $y<0$.
- Proof of $\sum_{k = 1}^{n} \frac{1}{k^{2}} < 2 - \frac{1}{n}$
- Finding an equation of circle which passes through three points
- How to Expand Into Partial Fractions
- Why rationalize the denominator?
- Apparently cannot be solved using logarithms
- Finding how multiplication and addition behave on $\mathbb{F}_4$ without any result
- Need help with continuing an idea concerning showing that $4\sum\limits_{n \ge 1} a_n^2 \ge \sum\limits_{n \ge 1} \frac1{n^2}(a_1+…+a_n)^2 $

Hint: in that interval,

$$(1-a)(1-b) \ge 0$$

$$ab-a-b+1=(a-1)(b-1)\ge 0$$ since $a-1\le0$ and $b-1\le 0$.

- Is empty set a proper subset of itself?
- Probability Theory – Fair dice
- An eigenvector is a non-zero vector such that…
- More Generating Functions problems
- Are these two definitions equivalent?
- Sampling $Q$ uniformly where $Q^TQ=I$
- derivation of simple linear regression parameters
- Euler-Maclaurin Summation Formula for Multiple Sums
- Do these $\sigma$-algebras on second countable spaces coincide?
- For field extensions $F\subsetneq K \subset F(x)$, $x$ is algebraic over $K$
- How to solve $x+\sin(x)=b$
- Conjugacy Class of Isomorphisms Between Two Isomorphic Groups Definition
- How prove this inequality $\sum\limits_{cyc}\frac{x^2}{(2x+y)(2x+z)}\le\frac{1}{3}$
- $I+J=R$, where $R$ is a commutative rng, prove that $IJ=I\cap J$.
- How did Beltrami show the consistency of hyperbolic geometry in his 1868 papers?