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Understanding Limits: Graphical and Numerical Approaches in Calculus

This section explores the concept of limits in calculus, emphasizing their importance and utility. It provides examples of how to estimate limits using tables of values and graphical representations. Theorems involving limits, including those related to trigonometric, exponential, and logarithmic functions, are presented with practical examples to solidify understanding. Students will learn to evaluate limits analytically and discover the significance of the Squeeze Theorem. Engaging with these concepts will enhance comprehension of calculus principles and their applications.

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Understanding Limits: Graphical and Numerical Approaches in Calculus

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  1. Section 2.2 Finding Limits Graphically & Numerically

  2. What’s the point of Calculus?

  3. What’s the point of Calculus?

  4. What’s the point of Calculus?

  5. What’s the point of Calculus?

  6. The Concept of a “Limit”

  7. Example 1 Use a table of values to estimate the limit. Confirm graphically.

  8. Example 2 (#18-26 even in your book)

  9. Example 2 (cont.) (#18-26 even in your book)

  10. Example 2 (cont.) (#18-26 even in your book)

  11. Example 3 (#28 in your book)

  12. Example 4 (#30 in your book) Use the graph of to identify the values of for which exists.

  13. Example 5 Sketch a graph of a function with the given properties. DNE

  14. Section 2.3 Evaluating Limits Analytically

  15. Theorems Involving Limits

  16. Theorems Involving Limits

  17. Theorems Involving Limits (cont.)

  18. Theorems Involving Limits

  19. Example 1 Find .

  20. Example 2 Find .

  21. Example 3 Find .

  22. Example 4 Find .

  23. Other Theorems Involving Limits • Theorem 2.6 deals with finding the limits of trigonometric, exponential, and logarithmic functions. • Theorem 2.7 talks about fnc.’s that agree at all but one point. • Theorem 2.8 is the Squeeze Theorem.

  24. Example 5 Find .

  25. Example 5 Find given .

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