A function is continuous when its graph is a single unbroken curve ... that you could draw without lifting your pen from the paper.

Nov 16, 2022 · In this section we will introduce the concept of continuity and how it relates to limits. We will also see the Intermediate Value Theorem in this section and how it can be used to determine if …

Studying about the continuity of a function is really important in calculus as a function cannot be differentiable unless it is continuous. Let us study more about the continuity of a function by knowing …

Nov 22, 2025 · Here we use Algebraic tricks such as factorization, the use of Trigonometric Identities, etc to solve continuity-related problems. Let us elaborate with the help of an example. Example: Let f …

Jun 6, 2025 · This article showed how to tell if a function is continuous at a single point, as well as 1.12 confirming continuity over an interval. It also covered LIM-2.B.1 and LIM-2.B.2 for AP® Calculus AB …

For a function to be continuous at a point, it must be defined at that point, its limit must exist at the point, and the value of the function at that point must equal the value of the limit at that point. …

But a function is a relationship between numbers. (Topic 3 of Precalculus.) Any definition of a continuous function therefore must be expressed in terms of numbers only. To do that, we must see what it is …

Problem: Let $f (x)=5x$ when $x\le 2$, and let $f (x)=a^2x^2-7x$ when $x>2$. Find all values of $a$ such that $f$ is continuous everywhere. Solution: Note that since $5x$ is continuous everywhere, $f$ …

In calculus, a continuous function is a real-valued function whose graph does not have any breaks or holes. Continuity lays the foundational groundwork for the intermediate value theorem and extreme …

For the past two weeks, we’ve talked about functions and then about limits. Now we’re ready to combine the two and talk about continuity and the various ways it can fail. Given a \nice" function f(x), such as …