Elementary Calculus: An Infinitesimal Approach, 2nd Edition by H. Jerome Keisler

By H. Jerome Keisler

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Has slope 3 and y-intercept Ϫ5 54. Has x-intercept 3 and y-intercept Ϫ5 55. Passes through (3, Ϫ5) and is parallel to the line with equation 2x ϩ 3y ϭ 12 56. Is perpendicular to the line with equation y ϭ Ϫ3x Ϫ 5 and has y-intercept 7 57. Passes through (Ϫ2, Ϫ4) and is perpendicular to the line with equation 3x Ϫ y Ϫ 4 ϭ 0 64. 2x Ϫ y ϭ 1 and 65. x Ϫ 3y ϭ Ϫ1 and 3x ϩ 2y ϭ 12 4x ϩ 3y ϭ 11 66. Find the distance between the points. a. (1, 3) and (4, 7) b. (1, 0) and (4, 4) c. (Ϫ1, 3) and (4, 9) d. (Ϫ2, 1) and (10, 6) 67.

We could very well have defined this function by giving the rule as f(t) ϭ 1t or f(u) ϭ 1u. In other words, it doesn’t matter what letter we choose to represent the independent variable when describing the rule for a function. Indeed, we can describe the rule for f using the expression f( ) ϭ 1( )ϭ( )1>2 To find the value of f at x, we simply insert x into the blank spaces inside the parentheses! As another example, consider the function t defined by the rule t(x) ϭ 2x 2 ϩ x. We can describe the rule for t by t( ) ϭ 2( )2 ϩ ( ) obtained by replacing each x in the expression for t(x) by a pair of parentheses.

If this gap between women’s and men’s wages continued to narrow linearly, what percent of men’s wages were women’s wages at the beginning of 2004? Source: Journal of Economic Perspectives. 83. Show that only those points satisfying Equation (3) can lie on the line L passing through P1(x 1, y1) with slope m. 84. Show that Equation (6) also holds when 90° Ͻ f Ͻ 180°. In Exercises 85–88, determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that shows it is false.

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