Page 2: Advanced Concepts and Numerical Approximations

This page delves into more advanced aspects of calculating the momentane Änderungsrate, focusing on numerical approximations and limit concepts.

The page presents a table or matrix of values, likely representing different approximations of the momentane Änderungsrate as the step size (h) approaches zero. This method is known as the limit definition of the derivative.

Key points on this page include:

• The use of small increments (h) to approximate the momentane Änderungsrate
• Values ranging from -0.999 to -1.01, suggesting a convergence towards -1
• The presence of very small values like 0.001 and 0.01, indicating precision in calculations

Vocabulary: "h" in this context typically represents the step size or increment used in numerical approximations of derivatives.

Definition: The momentane Änderungsrate is the limit of the average rate of change as the interval approaches zero.

Highlight: The table demonstrates how the approximation of the momentane Änderungsrate becomes more accurate as the step size (h) decreases.

This page emphasizes the importance of understanding limit concepts in calculus and how they relate to finding the momentane Änderungsrate. It also illustrates the practical application of numerical methods in approximating derivatives when exact analytical solutions are not readily available.