Intereting Posts

How many real roots does $(x-a)^3+(x-b)^3+(x-c)^3$ have?
Prove $\sum_{i=1}^n i! \cdot i = (n+1)! – 1$?
First four terms of the power series of $f(z) = \frac{z}{e^z-1}$?
Uniqueness of Tetration
Inverse Laplace of $ \frac{1}{\sqrt{s} – 1} $?
Calculate coordinate of any point on triangle in 3D plane
Some ways to get a set of primes
Name of this identity? $\int e^{\alpha x}\cos(\beta x) \space dx = \frac{e^{\alpha x} (\alpha \cos(\beta x)+\beta \sin(\beta x))}{\alpha^2+\beta^2}$
Question Relating with Open Mapping Theorem for Analytic Functions
equality of two operators…
Floor and Ceiling function
Find $\lim\limits_{n \to \infty}\left(1-\frac{1}{2^2}\right)\left(1-\frac{1}{3^2}\right)\cdots\left(1-\frac{1}{n^2}\right)$
$\exists\text{ set }X:X=X^X$?
Subadditivity of Lebesgue-Stieltjes measure
Solving this integral $\int\frac{1}{1+x^n} dx$?

can we do this without integration ( breaking the area into triangles & rectangles etc ) ?

- How to show that $6^n$ always ends with a $6$ when $n\geq 1$ and $n\in\mathbb{N}$
- Denesting Phi, Denesting Cube Roots
- finding the value of x from a complex form of absolute value
- $x^{2000} + \frac{1}{x^{2000}}$ in terms of $x + \frac 1x$.
- General misconception about $\sqrt x$
- How to show that $\frac{x^2}{x-1}$ simplifies to $x + \frac{1}{x-1} +1$

- How to prove this binomial identity $\sum_{r=0}^n {r {n \choose r}} = n2^{n-1}$?
- Find the area of largest rectangle that can be inscribed in an ellipse
- Area of a parallelogram, vertices $(-1,-1), (4,1), (5,3), (10,5)$.
- What is the relationship between the lengths of the binary and decimal representations of a number?
- equation $\frac{\frac{1}{x^2}-\frac{1}{y^2}}{\frac{1}{x^2}+\frac{1}{y^2}}$
- Differentiation using first principles with rational powers
- Why is a raised to the power of Zero is 1?
- Division by $0$
- Show that $x^3y^3(x^3+y^3) \leq 2$
- Fact about polynomials

Note the three similar right triangles. One below the top line, another below the bottom line and one above the $y=1$

The area of the biggest right triangle is $\frac{\frac{3}2\frac32}2=\frac98$

You have to subtract the area of other two (white ones) from this one,

The bottom one has $\frac{\frac{3}4\frac34}2=\frac9{32}$

The top one has $\frac{\frac{1}2\frac12}2=\frac1{8}$

Finally you have $\frac98-\frac{1}{8}-\frac9{32}=\frac{23}{32}$

- Proof of the following fact: $f$ is integrable, $U(f,\mathcal{P})-L(f,\mathcal{P})<\varepsilon$ for any $\varepsilon>0$
- Prove two parallel lines intersect at infinity in $\mathbb{RP}^3$
- Describe all integers a for which the following system of congruences (with one unknown x) has integer solutions:
- $G$ is $p$-supersoluble iff $|G : M | = p$ for each maximal subgroup $M$ in $G$ with $p | |G : M |$.
- Does there exist two non-constant polynomials $f(x),g(x)\in\mathbb Z$ such that for all integers $m,n$, gcd$(f(m),g(n))=1$?
- Nicer expression for the following differential operator
- Number of functions $f:\times\rightarrow$
- Equivalent form of definition of manifolds.
- A theorem due to Gelfand and Kolmogorov
- Find all irreducible monic polynomials in $\mathbb{Z}/(2)$ with degree equal or less than 5
- Proof the degree of a reflection through a hyperplane is −1.
- lim inf $|a_n|=0 \implies \sum_{k=1}^\infty a_{n_k}$ converges
- Solution of a 2nd order differential equation
- Understanding this proof that a polynomial is irreducible in $\mathbb{Q}$
- Decidability of the Riemann Hypothesis vs. the Goldbach Conjecture