# Ch 5: Continuity in AP Calculus: Homework Help Resource

### About This Chapter

## How it works:

- Identify which concepts are covered on your continuity in AP calculus homework.
- Find videos on those topics within this chapter.
- Watch fun videos, pausing and reviewing as needed.
- Complete sample problems and get instant feedback.
- Finish your continuity homework with ease!

## Topics from your homework you'll be able to complete:

- Continuity in a function
- Discontinuities in functions and graphs
- Regions of continuity in a function
- Intermediate Value Theorem definition and applications

### 1. Continuity in a Function

Continuity is the state of an equation or graph where the solutions form a continuous line, with no gaps on the graph. Learn the concept of continuity, opposed by discontinuity, and examples of both types of functions.

### 2. Discontinuities in Functions and Graphs

A discontinuity is where the potential values in an equation 'jump', rather than being continuous as with an un-broken line on a graph. See how discontinuities appear in graphs and equations, including jump discontinuities and asymptotic discontinuities.

### 3. Regions of Continuity in a Function

A region of continuity is where you have a function that is continuous and is a critical understanding in calculus and mathematics. Learn more about regions of continuity as a function and read examples.

### 4. Intermediate Value Theorem: Definition

The intermediate value theorem concerns the properties of continuous functions over a range and finding at least one solution. Learn more about the definition of the intermediate value theorem using the altitudes of a jet airplane as an example.

### 5. Intermediate Value Theorem: Examples and Applications

The intermediate value theorem states that a function, when continuous, can have a solution for all points along the range that it is within. Identify the applications of this theorem in finding roots, and solve some example functions.

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### Other Chapters

Other chapters within the AP Calculus AB & BC: Homework Help Resource course

- Functions in AP Calculus: Homework Help Resource
- Graphing and Functions in AP Calculus: Homework Help Resource
- Sequences and Series in AP Calculus: Homework Help Resource
- Limits in AP Calculus: Homework Help Resource
- Exponentials and Logarithms in AP Calculus: Homework Help Resource
- Exponents and Polynomials in AP Calculus: Homework Help Resource
- Applications of Derivatives in AP Calculus: Homework Help Resource
- Calculating Derivatives and Derivative Rules in AP Calculus: Homework Help Resource
- Differential Equations in AP Calculus: Homework Help Resource
- Area Under the Curve and Integrals in AP Calculus: Homework Help Resource
- Graphing Derivatives and L'Hopital's Rule in AP Calculus: Homework Help Resource
- Integration and Integration Techniques in AP Calculus: Homework Help Resource
- Integration Applications in AP Calculus: Homework Help Resource
- Rate of Change in AP Calculus: Homework Help Resource
- Geometry and Trigonometry in AP Calculus: Homework Help Resource
- How to Use Scientific Calculators for AP Calculus: Homework Help Resource