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

Figure 1.3: The positions and slopes of four secants through point P on the heat shield graph.

Figure 1.4: The tangent line at point P has the same steepness (slope) that the curve has at P.

Figure 1.8: The functions in Example 7.

Figure 1.11: The relation of  and  in the definition of limit.

Figure 1.13: An open interval of radius 3 about x0 = 5 will lie inside the open interval (2, 10).

Figure 1.14: The function and intervals in Example 10.

Figure 1.19: The Sandwich Theorem confirms that (a) lim0 sin = 0 and (b) lim 0 (1 – cos) = 0.

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)

Figure 1.24: The graph of f () = (sin )/.

Figure 1. 25: The figure for the proof of Theorem 6 Figure 1.25: The figure for the proof of Theorem 6. TA/OA = tan  , but OA = 1, so TA = tan .

Figure 1.27: The function in Example 3.

Figure 1.29: The function in Example 5(a).

Figure 1.37: The graph of y = e1/x for x < 0 shows limx0– e1/x = 0. (Example 11)

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)

Figure 1.50: The function in (a) is continuous at x = 0; the functions in (b) through ( f ) are not.

Figure 1.53: Composites of continuous functions are continuous.

Figure 1.62: The tangent slope is f (x0 + h) – f (x0) h lim h0