Ch 18: NYSTCE Mathematics: Calculus Concepts

About This Chapter

Learn about calculus concepts in this chapter of the NYSTCE Mathematics exam study guide. Video lesson and self-assessment quizzes teach you all you need to know about mathematics for teacher licensure in New York.

NYSTCE Mathematics: Calculus Concepts - Chapter Summary

Lessons in this chapter explore calculus concepts, including using a graph to define limits, using notation, and one-sided limits and continuity. How to determine the limits of functions, understanding the properties of limits, and defining asymptotes and infinity are also discussed. Additionally, by the end of this chapter, you should be familiar with:

  • Derivatives
  • How to use Riemann sums for functions and graphs
  • How to find the limits of Riemann sums
  • Definite integrals
  • How to use Riemann sums to calculate integrals
  • The fundamental theorem of calculus
  • Slopes and tangents on a graph

Short, engaging video lessons thoroughly explain each subject, and the jump feature under the Timeline tab allows you to skip directly to main subjects within the video lessons. Knowledgeable instructors are available to answer any questions you may have. Visit your dashboard to track your progress through the course.

14 Lessons in Chapter 18: NYSTCE Mathematics: Calculus Concepts
Test your knowledge with a 30-question chapter practice test
Using a Graph to Define Limits

1. 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.

Understanding Limits: Using Notation

2. 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.

One-Sided Limits and Continuity

3. One-Sided Limits and Continuity

Over the river and through the woods is only fun on a continuous path. What happens when the path has a discontinuity? In this lesson, learn about the relationship between continuity and limits as we walk up and down this wildlife path.

How to Determine the Limits of Functions

4. How to Determine the Limits of Functions

You know the definition of a limit. You know the properties of limits. You can connect limits and continuity. Now use this knowledge to calculate the limits of complex functions in this lesson.

Understanding the Properties of Limits

5. Understanding the Properties of Limits

Graphically we can see limits, but how do we actually calculate them? Three words: Divide and Conquer. In this lesson, explore some of the properties that we can use to find limits.

Graphs and Limits: Defining Asymptotes and Infinity

6. Graphs and Limits: Defining Asymptotes and Infinity

Infinity is a hard concept to understand and the word asymptote is pretty intimidating. But this fun lesson will make both seem like a walk in the park as it defines both and shows their relationship using a graph.

Derivatives: The Formal Definition

7. Derivatives: The Formal Definition

The derivative defines calculus. In this lesson, learn how the derivative is related to the instantaneous rate of change with Super C, the cannonball man.

Derivatives: Graphical Representations

8. 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.

How to Use Riemann Sums for Functions and Graphs

9. How to Use Riemann Sums for Functions and Graphs

Find out how Riemann sums can be used to calculate multiple areas efficiently. In this lesson, you'll learn how this can come in handy for irregular areas and how you can put it to use.

How to Find the Limits of Riemann Sums

10. How to Find the Limits of Riemann Sums

What would happen if you could draw an infinite number of infinitesimally thin rectangles? You'd get the exact area under a curve! Define the Holy Grail of calculus, the integral, in this lesson.

Definite Integrals: Definition

11. 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.

How to Use Riemann Sums to Calculate Integrals

12. How to Use Riemann Sums to Calculate Integrals

As a new property owner, you might relish mowing your lawn. Up and down your property you mow and measure out small sections to find the area of your property. In this lesson, you will discover what a Riemann sum approach is and how to calculate an estimated area using multiple slices.

The Fundamental Theorem of Calculus

13. The Fundamental Theorem of Calculus

The fundamental theorem of calculus is one of the most important equations in math. In this lesson we start to explore what the ubiquitous FTOC means as we careen down the road at 30 mph.

Slopes and Tangents on a Graph

14. Slopes and Tangents on a Graph

Hit the slopes and learn how the steepness of a line is calculated. Calculate the slopes between points and draw the tangents of curves on graphs in this lesson.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
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Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
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Other Chapters

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