Calculus - Introduction to Limits and Limit Laws

Vocabulary flashcards covering fundamental definitions, algebraic identities, and limit laws from the introductory calculus lecture.

Limit of a Function

The value $L$ that $f(a)$ is expected to be, defined such that $f(x)$ can be made as close to $L$ as desired by restricting $x$ to be close enough to $a$ without $x$ being equal to $a$.

Limit (as an operation)

A function or operation whose inputs are functions and whose outputs are real numbers.

Piecewise Defined Function

A function defined using different rules for different intervals or values of its input, serving as an important source of examples in calculus.

Difference of Squares Formula

The algebraic formula $a^2 - b^2 = (a - b)(a + b)$, which serves as a critical algebraic tool for simplifying limits involving radicals or polynomials.

Sum Law

A limit rule stating that the limit of a sum is equal to the sum of the limits, allowing the exchange of the order of operations between addition and evaluating limits.

Constant Multiple Law

A limit rule that allows exchanging the order of operations between taking a limit and multiplying a function by a constant factor.

Identity Law

The limit rule stating that the limit of $x$ as $x$ approaches $a$ is equal to $a$.