https://spherical-harmonics.hateblo.jp/entry/2025/01/21/163451

2025.01.21記

[1] Find the remainder when
$f(x)=a_0x^n+a_1x^{n-1}+\cdots+a_{n-1}x+a_n$
is devided by $(x-\alpha)(x-\beta)$ .

[2] Prove that the triangle of maximum area inscribed in a given circle is an equilateral triangle.

[3] Find the length of the arc of the parabola $y^2=4ax$ from the vertex to the end of the latus-rectum.

[4] A car is moving with velocity $v$ and acceleration $\alpha$ on a circular track of radius $r$ . What is inclination of the plumb line hung from the ceiling of the car ?