By Howard Anton, Irl C. Bivens, Stephen Davis

The 9th variation keeps to supply engineers with an obtainable source for studying calculus. The publication comprises rigorously labored examples and precise challenge varieties that support enhance comprehension. New utilized routines exhibit the usefulness of the math. extra precis tables with step by step information also are included into the chapters to make the thoughts more uncomplicated to appreciate. the fast cost and concentrate on suggestions routines were up to date to boot. Engineers turn into engaged within the fabric as a result easy-to-read type and real-world examples.

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A curve is symmetric about the origin if for each point (x, y) on the graph, the point (—x, —y) is also on the graph. ) This suggests the following symmetry tests. Explain why the graph of a nonzero function cannot be symmetric about the jr-axis. 3 Symmetric about the y-axis Symmetric about j the origin THEOREM (Symmetry Tests) (a) A plane curve is symmetric about the y-axis if and only if replacing x by —x in its equation produces an equivalent equation. (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.

Y= l / x . y = 1/Jt4 y=l/x6. 5 INVERSE PROPORTIONS Recall that a variable y is said to be inversely proportional to a variable x if there is a positive constant k, called the constant of proportionality, such that (1) Since k is assumed to be positive, the graph of (1) has the same shape as y = l/x but is compressed or stretched in the ^-direction. Also, it should be evident from (1) that doubling x multiplies y by 1, tripling x multiplies y by |, and so forth. Equation (1) can be expressed as xy = k, which tells us that the product of inversely proportional variables is a positive constant.

E) /GO = — x 1+* 2 (f) f(x) = 2 60. Suppose that the function / has domain all real numbers. Determine whether each function can be classified as even or odd. Explain. r-axis and reflecting about the jc-axis the portion that lies below the x-axis. Use this method to obtain the graph of y = 2x — 3| from the graph of y = 2x — 3. 68-69 Use the method described in Exercise 67. 68. Sketch the graph of y = 1 - x2\. 3 Families of Functions 69. Sketch the graph of (a) f(x) = \cosx\ (b) /CO = cos x + | cos x |.

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