Explanation

The derivative of y = x² is dy/dx = 2x.

At x = 2, the slope is 2(2) = 4.

The tangent line equation is y - 4 = 4(x - 2), which simplifies to y = 4x - 4, or 4x - y = 4.

Explanation

To determine the type of conic section, rewrite the equation in standard form:

9x² + 4y² = 36

Divide by 36:

x²/4 + y²/9 = 1

Since 9 > 4, the major axis is vertical.

Explanation

Non-terminating repeating decimals can be expressed as fractions, so they are rational numbers.

In contrast, irrational numbers have non-terminating, non-repeating decimal expansions.

Explanation

A critical point occurs where the derivative of a function is zero or does not exist.

These points are important for finding local maxima, minima, or points of inflection.

Explanation

A sequence is a function whose domain is the set of natural numbers (1, 2, 3, ...).

Each natural number input gives a specific term in the sequence.

Explanation

The ratio test and root test are inconclusive when the limit of the ratio (or root) of successive terms is exactly 1.

These tests fail to determine convergence or divergence in this case.

Explanation

A quadratic equation has the form ax² + bx + c = 0, and it typically has two roots. 

These roots can be real or complex, and they can be distinct or repeated (in the case of a double root).

Explanation

A matrix has an inverse only if its determinant is non-zero, meaning it is non-singular.

Singular matrices (with determinant = 0) do not have an inverse.

Explanation

Mean Value Theorem applies to functions that are continuous on a closed interval [a, b].

And differentiable on the open interval (a, b).

Explanation

A parabola is defined as the set of points equidistant from a fixed point (focus) and a fixed line (directrix).

Its eccentricity (e) = 1, which distinguishes it from ellipses (e < 1) and hyperbolas (e > 1).