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49 Questions

Knowing that for any set of real numbers $x,y,z$, such that $x+y+z = 1$ the inequality $x^2+y^2+z^2 \ge \frac{1}{3}$ holds.

Finding the limit $\lim_{n\to \infty} \left({\frac{n+1}{n-2}}\right)^\sqrt n$

Rational numbers inequality proof - is this proof valid?

Finding $\lim_{x\to -2}{\frac{x+2}{\sqrt{-x-1}-1}}\;$ without L'Hospital

$x + y = 7 $and $x^3 - y^3 = 37$, find $xy$

Evaluating $\lim_{x \to 0}{\frac{\sin(4x)}{\sin(3x)}}$ without L'Hospital

Evaluating $\lim_{n\to\infty}{n\left(\ln(n+2)-\ln n\right)}$

Absolute value equation with rational expression

Prove that three medians divide a triangle into 6 triangles with equal surface area.

Worker's security code - combinatorics

Is it possible to solve $x\sin(x) = 7$ algebraically?

Reflection over a line $y= ax + b$ - How to find the according point?

Chessboard - placing two kings

Probability - “tetrahedronal cube” - Probabiltiy that a number is a perfect cube - sample space

In how many ways can we get a one-pair-hand in Poker?

Deductive proof in natural numbers - division

Find seventh term of the evaluation of $(2a+b^2)^8$

Prove an inequality using Mean Value Theorem [duplicate]

Evaluating $\lim_{x\to1}{\frac{\sqrt{x^2+3}-2}{\sqrt{x^2+8}-3}}$ without L'Hospital's Theorem

Evaluating limit $\lim_{n\to\infty}({\sqrt{4^n + 3^n} - 2^n})$

Evaluating $\lim_{x\to 0}{\frac{\sin^2x}{2x^2}}$ without L'Hospital

Evaluating $\int \frac{\sin^2(x)}{1-\cos(x)} \, \text{d}x$.

For what values of parameter m the function $g(x) - 2x^3 - 3x^2 + mx + 3 $ has an extremum of 10? An easier way to solve it

Exploiting the ambiguity of the notation $sin2x$

How many ways are there to form a $4$-digit from $2$ unique digits? - A question

Given $a = \log_{\sqrt{6}}{\sqrt[3]{4}}$ find $\log_{\sqrt{3}}{\sqrt[3]{2}}$

Triangle - length of the sides - proof

If triangle's angles are $\alpha \leq \beta \leq \gamma$, then respective opposite sides are $a \leq b \leq c$. How to handle obtuse case?

Distributing $10$ unique candies to $2$ kids - two models

Angle bisector in a trapezoid - surface area ratio