Calculus I Lecture 1: Limits

These flashcards cover essential vocabulary and concepts related to limits as explained in the lecture notes.

Limit

A value that a function approaches as the input approaches some value.

$$ext{lim}_{x o a} f(x)$$

Notation for the limit of function f(x) as x approaches a.

Left-Hand Limit

The value that the function approaches as the input approaches from the left (denoted $ext{lim}_{x o a^-} f(x)$).

Right-Hand Limit

The value that the function approaches as the input approaches from the right (denoted $ext{lim}_{x o a^+} f(x)$).

Continuous Function

A function is continuous at a point if the left-hand limit, right-hand limit, and the function value at that point are all equal.

Piecewise Function

A function that is defined by different expressions based on the input value.

Limit Laws

Rules that allow us to evaluate limits more easily (e.g., algebraic operations can be applied to limits).

Limit Evaluation

The process of finding the limit of a function as the variable approaches a certain value.

Graphical Limit

Using a graph to determine the limit values by observing the behavior of the function as the input approaches a specific point.

Example Limit

Evaluate $ext{lim}_{x o 2} (2x + 3)$ which equals 7.