# Ch 19: ILTS Mathematics: Calculus

### About This Chapter

## ILTS Mathematics: Calculus- Chapter Summary

Examine the text and video lessons found in this chapter on calculus. You will study what calculus is and operations involving calculus principles, putting you closer to being prepared to take the ILTS Mathematics exam. This chapter's topics include:

- Graphing to define and understand limits
- Continuity in a function
- Horizontal and vertical asymptotes
- Arithmetic series in algebra
- Differential calculus
- Optimization and differentiation
- Indefinite and definite integrals
- Integration and dynamic motion
- Calculating volumes using single integrals
- Simple areas with root finding and integration
- The area between functions with integration
- Derivatives

The resources that you will find in this chapter include text lessons, lesson videos, multiple-choice quizzes, lesson transcripts, and a chapter test. Each of these are designed and organized in a manner that sets you up for success on your exam day. You can access these resources as many times as you need to, on a computer, smartphone or tablet. The material found in this chapter can be a bit complicated, so reviewing it multiple times can help reinforce it and make it easier to recall.

### 1. What is Calculus? - Definition & History

In this lesson, you're going to learn about some of the history of calculus: who discovered it, and the three major stages with which it developed through time.

### 2. Using a Graph to Define Limits

My mom always said I tested the limits of her patience. Use graphs to learn about limits in math. You won't get grounded as we approach limits in this lesson.

### 3. Understanding Limits: Using Notation

Join me on a road trip as we define the mathematical notation of limits. As time goes by and I traverse hills and highways, the limit of my speed changes. Learn how to write these limits in this lesson.

### 4. Continuity in a Function

Travel to space and explore the difference between continuous and discontinuous functions in this lesson. Learn how determining continuity is as easy as tracing a line.

### 5. Horizontal and Vertical Asymptotes

No matter how hard you try to get to them, asymptotes remain out of reach. Learn about these invisible lines on graphs that show you places your equations just can't go.

### 6. Understanding Arithmetic Series in Algebra

In this video lesson, we will learn about arithmetic series and how they work. Learn also how to find the pattern of an arithmetic sequence along with finding the sum.

### 7. Differential Calculus: Definition & Applications

This lesson is an introduction to differential calculus, the branch of mathematics that is concerned with rates of change. If you ever wanted to know how things change over time, then this is the place to start!

### 8. Optimization and Differentiation

In this lesson, you can learn what optimization means from a mathematical standpoint. Using the techniques taught in this lesson, you can use the five steps to optimization to figure out practical things, like how much sleep you need to get before an exam.

### 9. Indefinite Integral: Definition, Rules & Examples

In this lesson, you will learn about the indefinite integral, which is really just the reverse of the derivative. We will discuss the definition, some rules and techniques for finding indefinite integrals, as well as a few examples.

### 10. Definite Integrals: Definition

Explore how driving backwards takes you where you've already been as we define definite integrals. This lesson will also teach you the relationship between definite integrals and Riemann sums. Then, discover how an integral changes when it is above and below the x-axis.

### 11. Integration and Dynamic Motion

This lesson uses driving to demonstrate how graphing can help you use calculus to figure out how fast you were going at a given time. Using this lesson, you can learn how to integrate your velocity to find your position.

### 12. How to Calculate Volumes Using Single Integrals

Ever wonder where the equation for the volume of a cone comes from? Or the equation for the volume of a sphere? In this lesson, learn how to use a slicing technique to find the volume of a region by solving a single integral.

### 13. How to Find Simple Areas With Root Finding and Integration

Combine your calculus tools in this lesson! Find the area enclosed by multiple arbitrary functions by first finding the root of an equation and then integrating over the resulting range.

### 14. How to Find Area Between Functions With Integration

Sometimes you aren't looking for the area under the curve; after all, not every region is between a curve and axis! In this lesson, learn how to find areas between curves as well as areas with complicated boundaries.

### 15. Derivatives: Graphical Representations

Take a graphical look at the definitive element of calculus: the derivative. The slope of a function is the derivative, as you will see in this lesson.

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### Other Chapters

Other chapters within the ILTS Mathematics (208): Test Practice and Study Guide course

- ILTS Mathematics: Concepts & Skills
- ILTS Mathematics: Logic & Reasoning
- ILTS Mathematics: Using Technology for Math
- ILTS Mathematics: Number Theory
- ILTS Mathematics: Solving Number Problems
- ILTS Mathematics: Real & Complex Numbers
- ILTS Mathematics: Measurement
- ILTS Mathematics: Multidimensional Objects
- ILTS Mathematics: Variables & Patterns
- ILTS Mathematics: Linear Relations & Functions
- ILTS Mathematics: Quadratic Relations & Functions
- ILTS Mathematics: Absolute Value
- ILTS Mathematics: Polynomials
- ILTS Mathematics: Radical Functions
- ILTS Mathematics: Rational Functions
- ILTS Mathematics: Exponential Functions
- ILTS Mathematics: Logarithmic Functions
- ILTS Mathematics: Trigonometric Functions
- ILTS Mathematics: Points, Lines, Planes & Space
- ILTS Mathematics: 2D & 3D Shapes
- ILTS Mathematics: Spatial Visualization
- ILTS Mathematics: Congruence, Similarity & Symmetry
- ILTS Mathematics: Probability Theory & Techniques
- ILTS Mathematics: Collecting & Representing Data
- ILTS Mathematics: Using Data to Make Predictions
- ILTS Mathematics Flashcards