1. Chapter 1. Finney Weir Giordano, Thomas’ Calculus, Tenth Edition © 2001. Addison Wesley Longman All rights reserved. Chapter 1, Slide 1 Finney Weir Giordano CHAPTER 1 Finney Weir Giordano, Thomas’ Calculus, Tenth Edition © 2001. Addison Wesley Longman All rights reserved.

2. Chapter 1. Finney Weir Giordano, Thomas’ Calculus, Tenth Edition © 2001. Addison Wesley Longman All rights reserved. Chapter 1, Slide 2 Figure 1.3: The positions and slopes of four secants through point P on the heat shield graph.

3. Chapter 1. Finney Weir Giordano, Thomas’ Calculus, Tenth Edition © 2001. Addison Wesley Longman All rights reserved. Chapter 1, Slide 3 Figure 1.4: The tangent line at point P has the same steepness (slope) that the curve has at P.

4. Chapter 1. Finney Weir Giordano, Thomas’ Calculus, Tenth Edition © 2001. Addison Wesley Longman All rights reserved. Chapter 1, Slide 4 Figure 1.8: The functions in Example 7.

5. Chapter 1. Finney Weir Giordano, Thomas’ Calculus, Tenth Edition © 2001. Addison Wesley Longman All rights reserved. Chapter 1, Slide 5 Figure 1.11: The relation of  and  in the definition of limit.

6. Chapter 1. Finney Weir Giordano, Thomas’ Calculus, Tenth Edition © 2001. Addison Wesley Longman All rights reserved. Chapter 1, Slide 6 Figure 1.13: An open interval of radius 3 about x 0 = 5 will lie inside the open interval (2, 10).

7. Chapter 1. Finney Weir Giordano, Thomas’ Calculus, Tenth Edition © 2001. Addison Wesley Longman All rights reserved. Chapter 1, Slide 7 Figure 1.14: The function and intervals in Example 10.

8. Chapter 1. Finney Weir Giordano, Thomas’ Calculus, Tenth Edition © 2001. Addison Wesley Longman All rights reserved. Chapter 1, Slide 8 Figure 1.19: The Sandwich Theorem confirms that (a) lim  0 sin  = 0 and (b) lim  0 (1 – cos  ) = 0.

9. Chapter 1. Finney Weir Giordano, Thomas’ Calculus, Tenth Edition © 2001. Addison Wesley Longman All rights reserved. Chapter 1, Slide 9 Figure 1.23: The function y = sin (1/x) has neither a right- hand nor a left-hand limit as x approaches zero. (Example 9)

10. Chapter 1. Finney Weir Giordano, Thomas’ Calculus, Tenth Edition © 2001. Addison Wesley Longman All rights reserved. Chapter 1, Slide 10 Figure 1.24: The graph of f (  ) = (sin  )/ .

11. Chapter 1. Finney Weir Giordano, Thomas’ Calculus, Tenth Edition © 2001. Addison Wesley Longman All rights reserved. Chapter 1, Slide 11 Figure 1.25: The figure for the proof of Theorem 6. TA/OA = tan , but OA = 1, so TA = tan .

12. Chapter 1. Finney Weir Giordano, Thomas’ Calculus, Tenth Edition © 2001. Addison Wesley Longman All rights reserved. Chapter 1, Slide 12 Figure 1.27: The function in Example 3.

13. Chapter 1. Finney Weir Giordano, Thomas’ Calculus, Tenth Edition © 2001. Addison Wesley Longman All rights reserved. Chapter 1, Slide 13 Figure 1.29: The function in Example 5(a).

14. Chapter 1. Finney Weir Giordano, Thomas’ Calculus, Tenth Edition © 2001. Addison Wesley Longman All rights reserved. Chapter 1, Slide 14 Figure 1.37: The graph of y = e 1/x for x < 0 shows lim x  0 – e 1/x = 0. (Example 11)

15. Chapter 1. Finney Weir Giordano, Thomas’ Calculus, Tenth Edition © 2001. Addison Wesley Longman All rights reserved. Chapter 1, Slide 15 Figure 1.42: The graph of f (x) = x + e –x looks like the graph of g(x) = x to the right of the y-axis and like the graph of h(x) = e –x to the left of the y-axis. (Example 14)

16. Chapter 1. Finney Weir Giordano, Thomas’ Calculus, Tenth Edition © 2001. Addison Wesley Longman All rights reserved. Chapter 1, Slide 16 Figure 1.50: The function in (a) is continuous at x = 0; the functions in (b) through ( f ) are not.

17. Chapter 1. Finney Weir Giordano, Thomas’ Calculus, Tenth Edition © 2001. Addison Wesley Longman All rights reserved. Chapter 1, Slide 17 Figure 1.53: Composites of continuous functions are continuous.

18. Chapter 1. Finney Weir Giordano, Thomas’ Calculus, Tenth Edition © 2001. Addison Wesley Longman All rights reserved. Chapter 1, Slide 18 Figure 1.62: The tangent slope is f (x 0 + h) – f (x 0 ) h h0h0 lim