Be seated before the bell rings

1. Be seated before the bell rings Be prepare : Have these things out DESK Warm-up (in your notes) Glue in learning targets homework HW: pg 47;4-6,9 All bags, purse, etc off desk

2. Class Room Rule and Procedures • Enter the classroom • Enter quietly, go to your seat. Take off hat. • No gum or food, except water • Materials (sharpen pencil) • Have homework out • Work on warm-up quietly. • Go over warmup/homwork • Homework quiz ? • During Class • Take notes • Remove backpack/purse off disk. • Participate/ Listen / no talking • Stay seated. Ask to move for any reason • Group Work • Follow Study Team Expectations • Stay in your seat • Leaving class • Only pack up the last min of class. • Pick up any trash around you • Straighten up your seats • Collect group hw- Turn in your homework in the turn-in basket.

3. Notebook First Page Table of content Page 1) 1-1 A preview of Calculus 1

4. Composition Book (Notebook ) Skip about 3 page 1 Table of content Page 1) 1-1 A Preview of Calculus 1

5. 1.1 A preview of calculus 1 What is calculus?

6. Two questions: • How do I find instantaneous rate of velocity? • 2) How do I find area of different shapes? http://www.ima.umn.edu/~arnold/calculus/secants/secants1/secants-g.html

7. What Is Calculus?

8. What Is Calculus? Calculus is the mathematics of change. For instance, calculus is the mathematics of velocities, accelerations, tangent lines, slopes, areas, volumes, arc lengths, centroids, curvatures, and a variety of other concepts that have enabled scientists, engineers, and economists to model real-life situations. Although precalculus mathematics also deals with velocities, accelerations, tangent lines, slopes, and so on, there is a fundamental difference between precalculus mathematics and calculus. Precalculus mathematics is more static, whereas calculus is more dynamic.

9. What do you think the graph of Mr. X’s travels will look like? Distance Time

10. The tangent line problem We want the slope of the tangent line because it represents rate

11. The Tangent Line Problem Except for cases involving a vertical tangent line, the problem of finding the tangent line at a point P is equivalent to finding the slope of the tangent line at P. You can approximate this slope by using a line through the point of tangency and a second point on the curve, as shown in Figure 1.2(a). Such a line is called a secant line. Figure 1.2 (a)

12. The Tangent Line Problem If P(c, f(c))is the point of tangency and is a second point on the graph of f, the slope of the secant line through these two points can be found using precalculus and is given by

13. The Tangent Line Problem As point Q approaches point P, the slopes of the secant lines approach the slope of the tangent line, as shown in Figure 1.2(b). When such a “limiting position” exists, the slope of the tangent line is said to be the limit of the slopes of the secant lines. Figure 1.2 (b)

14. The area problem https://www.youtube.com/watch?v=O2d26o8-jcI

15. The Area Problem As you increase the number of rectangles, the approximation tends to become better and better because the amount of area missed by the rectangles decreases. Your goal is to determine the limit of the sum of the areas of the rectangles as the number of rectangles increases without bound.

16. The Area Problem You can approximate the area of the region with several rectangular regions as shown in Figure 1.4. Figure 1.4

17. Example problems: Estimating area under curve https://www.youtube.com/watch?v=O2d26o8-jcI

18. Answer to the Two questions: • How do I find instantaneous rate of velocity? • 2) How do I find area of different shapes? We use secant lines to approximate slopes of tangent line . The slope of the tangent line is said to be the limit of the slopes of the secant line. We use rectangles to approximate area. We let the number of rectangles go to infinite