Daily Math · 2026-06-26

Question 1

The limit $\displaystyle\lim_{n 	o \infty} 2^n$ equals:

Accepted Answer

$2^n$ grows without bound: $\lim 2^n = \infty$.

Answer

$0$

Answer

$1$

Answer

$\infty$

Answer

does not exist

Question 2

The solution of $\begin{cases} x + y + z = 6 \ x - y = 0 \ y + z = 5 \end{cases}$ is:

Accepted Answer

$x = y$. Then $2y + z = 6$ and $y + z = 5$, so $y = 1$ and $z = 4$. Solution: $(1, 1, 4)$.

Answer

$(1, 1, 4)$

Answer

$(2, 2, 3)$

Answer

$(0, 0, 5)$

Answer

$(3, 3, 2)$

Question 3

On the power set $\mathcal{P}(X)$, the symmetric difference $A 	riangle B = (A \setminus B) \cup (B \setminus A)$ has identity:

Accepted Answer

$A 	riangle \emptyset = A$, so $\emptyset$ is the identity.

Answer

$\emptyset$

Answer

$X$

Answer

$\{x\}$ for some $x \in X$

Answer

no identity

Problems & worked solutions