Daily Math · 2026-06-15

Question 1

Find the term $T_7$ in the expansion of $\left(\sqrt[3]{x}+\dfrac{1}{\sqrt[4]{x}}\right)^{12}$.

Accepted Answer

$924\,x^{1/2}$

Answer

$C_{12}^6\,x$

Answer

$84\,x^{1/2}$

Answer

$C_{12}^6\,x^2$

Answer

$792\,x^{1/2}$

Answer

$924\,x$

Question 2

For $I_n = \displaystyle\int_0^1 \dfrac{x^n}{1 + x} \, dx$, the inequality $0 \le I_n \le \dfrac{1}{n + 1}$ holds because:

Accepted Answer

$\dfrac{1}{1 + x} \le 1$ on $[0, 1]$

Answer

$\dfrac{1}{1 + x} \ge 0$ on $[0, 1]$

Answer

$\dfrac{x^n}{1 + x} \le 1$ on $[0, 1]$

Answer

$\dfrac{x^n}{1 + x} \le x^n$

Question 3

The perpendicular bisector of the segment from $A(0, 0)$ to $B(4, 0)$ has equation:

Accepted Answer

$x = 2$

Answer

$y = 2$

Answer

$y = 0$

Answer

$x = 0$