Answer the following questions in mathematics: What type of function is f(x) = x2 + 5x + 6? State the Remainder Theorem. What are the conditions for a function to be continuous at a point? What is a s

The function $f(x) = x^2 + 5x + 6$ is a polynomial function of degree 2.

• Quadratic function

The Remainder Theorem states that if a polynomial $P(x)$ is divided by a linear divisor $(x-a)$, then the remainder is $P(a)$.

A function $f(x)$ is continuous at the point $x=a$ if and only if:

• $f(a)$ is defined.
• $\lim_{x \to a} f(x)$ exists.
• $\lim_{x \to a} f(x) = f(a)$.

A singular matrix is a square matrix whose determinant is zero.

• The determinant value of a singular matrix is 0.

Two lines with slopes $m_1$ and $m_2$ are parallel if and only if their slopes are equal.

• $m_1 = m_2$

A circle is formed when a plane intersects a cone perpendicular to the cone's axis.

The formula for $\cos 2\theta$ in terms of $\tan \theta$ is:

Given $\cos A = 1$. For an acute angle $A$:

• $0^\circ$

If $\beta$ is the angle between two vectors $\vec{p}$ and $\vec{q}$, the formula for $\cos \beta$ is:

For inversion, the relation between $OP$, $OP'$, and the radius $r$ is: