By Howard Anton

The 9th version keeps to supply engineers with an obtainable source for studying calculus. The ebook comprises conscientiously labored examples and unique challenge varieties that aid enhance comprehension. New utilized workouts display the usefulness of the maths. extra precis tables with step by step info also are integrated into the chapters to make the techniques more uncomplicated to appreciate. the short money and concentrate on recommendations workouts were up-to-date to boot. Engineers turn into engaged within the fabric a result of easy-to-read type and real-world examples.

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**Example text**

B) A plane curve is symmetric about the x-axis if and only if replacing y by −y in its equation produces an equivalent equation. (c) A plane curve is symmetric about the origin if and only if replacing both x by −x and y by −y in its equation produces an equivalent equation. 3 to identify symmetries in the graph of x = y 2 . y2 Solution. 8 x = y 2 . Thus, the graph is symmetric about the x-axis. The graph is not symmetric about the y-axis because replacing x by −x yields −x = y 2 , which is not equivalent to the original equation x = y 2 .

Explain what might cause breaks in the curve. (b) Suppose that a hospital patient receives an injection of an antibiotic every 8 hours and that between injections the concentration C of the antibiotic in the bloodstream decreases as the antibiotic is absorbed by the tissues. What might the graph of C versus the elapsed time t look like? 12. (a) If you had a device that could record the temperature of a room continuously over a 24-hour period, would you expect the graph of temperature versus time to be a continuous (unbroken) curve?

The domain of f + g is the intersection of the domains of f and g. 42. The domain of f ◦ g consists of all values of x in the domain of g for which g(x) = 0. 43. The graph of an even function is symmetric about the y-axis. 44. The graph of y = f (x + 2) + 3 is obtained by translating the graph of y = f(x) right 2 units and up 3 units. F O C U S O N C O N C E P TS 45. Use the data in the accompanying table to make a plot of y = f(g(x)). x −3 −2 −1 0 1 2 3 f (x) −4 −3 −2 −1 0 1 2 g(x) −1 0 1 2 3 −2 −3 Table Ex-45 46.