Daily Math · 2026-06-23

Question 1

The maximal domain of the function $f(x) = \sqrt{x - 2}$ is:

Accepted Answer

We need $x - 2 \ge 0$, i.e. $x \ge 2$. The domain is $[2, +\infty)$.

Answer

$\mathbb{R}$

Answer

$(-\infty, 2]$

Answer

$[2, +\infty)$

Answer

$(2, +\infty)$

Question 2

Find the $3	imes3$ determinant whose entries are all limit values (see problem image).

Accepted Answer

$\bullet$ Evaluate each of the nine limits to fill the matrix:

$$\begin{pmatrix}\sqrt{3}/2 & 2 & 1\ 3 & 4 & 4\ 0 & 3 & 1\end{pmatrix}$$

$\bullet$ Expand along row 1. The cofactor of the $(1,1)$ entry is $4\cdot 1-4\cdot 3=-8$:

$$	frac{\sqrt{3}}{2}\cdot(-8)=-4\sqrt{3}$$

$\bullet$ Cofactors of the $(1,2)$ and $(1,3)$ entries are $3\cdot 1-4\cdot 0=3$ and $3\cdot 3-4\cdot 0=9$:

$$-2\cdot 3+1\cdot 9=3$$

$\bullet$ Add the three contributions:

$$\det=3-4\sqrt{3}$$

Answer

$3-4\sqrt{3}$

Answer

$0$

Answer

$3+4\sqrt{3}$

Answer

$12$

Answer

$-4\sqrt3$

Answer

$3$

Question 3

$\displaystyle\sum_{n=1}^{\infty} \dfrac{1}{n^2}$ equals:

Accepted Answer

Euler's classical result: $\displaystyle\sum_{n=1}^{\infty}\dfrac{1}{n^2} = \dfrac{\pi^2}{6}$.

Answer

$	frac{\pi^2}{6}$

Answer

$	frac{\pi^2}{4}$

Answer

$	frac{\pi}{4}$

Answer

$1$

Problems & worked solutions