Let $\left\lfloor t \right\rfloor$ be the greatest integer less than or equal to $t$. Then the least value of $p \in \mathbb{N}$ for which
\[ \lim_{x \to 0^+} \left( x \left\lfloor \frac{1}{x} \right\rfloor + \left\lfloor \frac{2}{x} \right\rfloor + \dots + \left\lfloor \frac{p}{x} \right\rfloor \right) - x^2 \left( \left\lfloor \frac{1}{x^2} \right\rfloor + \left\lfloor \frac{2}{x^2} \right\rfloor + \dots + \left\lfloor \frac{9^2}{x^2} \right\rfloor \right) \geq 1 \]
is equal to __________.
A spherical mirror is a mirror which has been cut out of a spherical surface.
There are two kinds of spherical mirrors:
Concave mirrors are also called converging mirrors, because in these types of mirrors, light rays converge at a point after impact and reflect back from the reflective surface of the mirror.
The convex mirror has a reflective surface that is curved outward. Regardless of the distance between the subject and the mirrors, these mirrors are "always" virtual, upright and reduced.