Introduction_to_Limits_Mr_Anwar_Saad.pptx

Introduction_to_Limits_Mr_Anwar_Saad.pptx

1. Introduction to Limits Presented by Mr. Anwar Saad

2. Learning Objectives Understand the concept of a limit. Estimate limits graphically and numerically. Use proper mathematical notation for limits.

3. Warm-up: What happens near x = 2? Graph of f(x) = x² What is happening to f(x) as x gets close to 2 from both sides?

4. What is a Limit? Animation idea: point moving on a curve approaching x = 2. We care about where the function is heading, not necessarily where it lands.

5. Visualizing Limits Graph with a hole at x = 2. Table of x-values approaching 2 from both sides. Function value at x=2 is undefined, but limit exists.

6. Left-hand and Right-hand Limits Graph with two branches approaching different values. Define: lim x→2⁻ f(x), lim x→2⁺ f(x) If not equal, the limit does not exist.

7. Khan-Style Example Table with x: 1.9, 1.99, 1.999, 2.001, 2.01, 2.1 f(x) values shown approaching a limit. Ask: What is f(x) approaching?

8. Try It Yourself Graph of f(x) with a removable discontinuity. Question: Find lim x→3 f(x) Prompt: Discuss with your partner.

9. Real-Life Analogy Car approaching a red light but never stopping. Limit = destination; function value = actual position.

10. Exit Ticket Question: What is the limit of f(x) as x approaches 5? Small graph shown. Write answers on sticky notes or whiteboards.

11. Summary Limits describe behavior of a function near a point. Not about the actual value at that point. Graphs and tables help estimate limits visually and numerically.

12. Thank You Any questions? Presented by Mr. Anwar Saad