By Ron Larson, Bruce H. Edwards
The one Variable component of Calculus: Early Transcendental services, 5/e, bargains scholars leading edge studying assets. each version from the 1st to the 5th of Calculus: Early Transcendental capabilities, 5/e has made the mastery of conventional calculus talents a concern, whereas embracing the simplest positive aspects of latest expertise and, while acceptable, calculus reform principles.
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Additional info for Calculus of a Single Variable: Early Transcendental Functions
Describe the changes in the positions of the plotted points and the change in the equation of the line. 85. Tangent Line Find an equation of the line tangent to the circle x2 ϩ y2 ϭ 169 at the point ͑5, 12͒. 86. Tangent Line Find an equation of the line tangent to the circle ͑x Ϫ 1͒2 ϩ ͑ y Ϫ 1͒2 ϭ 25 at the point ͑4, Ϫ3͒. Distance In Exercises 87–92, find the distance between the point and line, or between the lines, using the formula for the distance between the point ͧx1, y1ͨ and the line Ax ؉ By ؉ C ؍0.
Y Ϫ 4 ϭ Ϫ 12͑x ϩ 1͒ x y * − y1* y2 − y1 m= 2 = x2* − x1* x2 − x1 d. y Ϫ 4 ϭ 0͑x ϩ 1͒ e. y Ϫ 4 ϭ 12͑x ϩ 1͒ Any two points on a nonvertical line can be used to determine its slope. f. y Ϫ 4 ϭ 1͑x ϩ 1͒ g. 14 Use your results to write an equation of a line passing through ͑Ϫ1, 4͒ with a slope of m. You can write an equation of a nonvertical line if you know the slope of the line and the coordinates of one point on the line. Suppose the slope is m and the point is ͑x1, y1͒. If ͑x, y͒ is any other point on the line, then y Ϫ y1 ϭ m.
2 ■ EXAMPLE 1 Evaluating a Function For the function f defined by f ͑x͒ ϭ x 2 ϩ 7, evaluate each of the following. a. f ͑3a͒ b. f ͑b Ϫ 1͒ c. f ͑x ϩ ⌬x͒ Ϫ f ͑x͒ , ⌬x ⌬x 0 Solution a. f ͑3a͒ ϭ ͑3a͒2 ϩ 7 ϭ 9a 2 ϩ 7 b. f ͑b Ϫ 1͒ ϭ ͑b Ϫ 1͒2 ϩ 7 ϭ b2 Ϫ 2b ϩ 1 ϩ 7 ϭ b2 Ϫ 2b ϩ 8 c. In calculus, it is important STUDY TIP to specify clearly the domain of a function or expression. For instance, in Example 1(c), the two expressions f ͑x ϩ ⌬ x͒ Ϫ f ͑x͒ ⌬x ⌬x 0 and 2x ϩ ⌬ x, are equivalent because ⌬ x ϭ 0 is excluded from the domain of each expression.