By Stanley I Grossman
1,178 pages plus Appendixes of 146 pages
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Extra info for Calculus
Casey runs a constant 30 ft/sec 58. 59. whether he hits a ground ball or a home run. Today in his first time at bat, he hit a home run. Write an expression for the function that measures his line-of-sight distance from second base as a function of the time t, in seconds, after he left home plate. Let f(x) be the fifth decimal place of the decimal expansion of x. 786543210) = 4, f( - 78. 90123456) = 3, and so on. Find the domain and range of f. S. money. S. currency. Describe each conversion function, and then show that one is not the inverse of the other.
Similarly, y = 4 when x = - 2 if y = x 2, and y = 4 when x = - 1 if y = (x - 1)2. By continuing in this manner, we can see that y values in the graph of y = x2 are the same as y values in the graph of y = (x - 1)2 except that they are achieved one unit later. Some representative values are given in Table 1. Thus we find that the graph of y = (x - 1)2 is the graph of y = x2 shifted one unit to the right. Similarly, in (e) we find that the graph of y = (x + 1)2 is the graph of y = x2 shifted one unit to the left.
27. 24. - + (b) *29. circles that meet at two distinct points. Show that the line through those two points of intersection has the equation - a)x + (B - b)y + (C c) = 0. Suppose the point (a, b) is on the circle x2 + y2 = 25. Show that the line determined by (a, b) and (5, 0) is perpendicular to the line determined by (a, b) and ( - 5, 0). Assume that b� o. Find the length of the common chord of these circles: (a) (x - a)2 (y - b)2 = R2 (b) (x -b)2 + (y - a)2 = R 2 Write an equation for a line that goes through the point (A, 0) and is tangent to the circle x2 + y2 = 1.