Limits and Continuity

Definition

Limits and continuity are fundamental concepts in calculus that deal with the behavior of functions as they approach certain values or points. Limits describe the value a function approaches as its input gets closer to a particular value, while continuity refers to the absence of any breaks, jumps, or holes in the graph of a function.

Related terms

Derivative:

The derivative of a function measures how fast it changes at each point and provides information about its slope or rate of change.

Infinite Limit:

An infinite limit occurs when the output of a function becomes infinitely large (positive or negative) as its input approaches a certain value.

Discontinuity:

A discontinuity is present in a function when there is an abrupt jump, hole, or vertical asymptote in its graph, indicating that it is not continuous at that point.