Daily Math · 2026-05-29

Question 1

The slant (oblique) asymptote of $f(x) = \dfrac{x^2 + 1}{x}$ as $x 	o \pm\infty$ is:

Accepted Answer

$f(x) = x + \dfrac{1}{x}$. As $x 	o \pm\infty$, $\dfrac{1}{x} 	o 0$, so the slant asymptote is $y = x$.

Answer

$y = 1$

Answer

$y = x$

Answer

$y = x^2$

Answer

$y = x + 1$

Question 2

For the geometric progression $(b_n)_{n \ge 1}$ with $b_1 = 2$ and $q = \sqrt{5}$, compute $\left\lfloor b_4 \right\rfloor$ (the integer part of $b_4$).

Accepted Answer

$b_4 = 10\sqrt{5}$. Since $\sqrt{5} \approx 2.236$, $b_4 \approx 22.36$, so $\lfloor b_4 \rfloor = 22$.

Answer

$20$

Answer

$21$

Answer

$22$

Answer

$25$

Question 3

On $\mathcal{P}(X)$ with symmetric difference, the inverse of any set $A$ is:

Accepted Answer

Every element is its own inverse: $A 	riangle A = \emptyset$.

Answer

$A$ itself

Answer

$X \setminus A$

Answer

$\emptyset$

Answer

$X$

Problems & worked solutions

Problem 1 — Asymptotes

Problem 2 — Geometric Sequences

Problem 3 — Binary Operations