By Soo T. Tan

Taking a clean procedure whereas conserving vintage presentation, the Tan Calculus sequence makes use of a transparent, concise writing variety, and makes use of correct, actual global examples to introduce summary mathematical options with an intuitive strategy. based on this emphasis on conceptual realizing, each one workout set within the 3 semester Calculus textual content starts off with proposal questions and every end-of-chapter assessment part contains fill-in-the-blank questions that are important for gaining knowledge of the definitions and theorems in each one bankruptcy. also, many questions requesting the translation of graphical, numerical, and algebraic effects are integrated between either the examples and the workout units. The Tan Calculus 3 semester textual content encourages a true international, software established, intuitive figuring out of Calculus with no comprising the mathematical rigor that's beneficial in a Calculus textual content.

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**Extra resources for Calculus: Early Transcendentals **

**Example text**

Y 2 1 Ϫ2 Ϫ1 0 58. A plane departs from Logan Airport in Boston bound for Heathrow Airport in London, a 6-hr, 3267-mi flight. After takeoff, the plane climbs to a cruising altitude of 35,000 ft, which it maintains until its descent to the airport. While at its cruising altitude, the plane maintains a ground speed of 550 mph. Let D ϭ f(t) denote the distance (in miles) flown by the plane as a function of time (in hours), and let A ϭ t(t) denote the altitude (in feet) of the plane. a. Sketch a graph of f that could describe the situation.

69. Show that an equation of the line L that passes through the points (a, 0) and (0, b) with a 0 and b 0 can be written in the form y x ϩ ϭ1 a b This is called the intercept form of the equation of L. 70. Use the result of Exercise 69 to find an equation of the line with x-intercept 2 and y-intercept 5. 71. Use the result of Exercise 69 to find an equation of the line passing through the points (Ϫ4, 0) and (0, Ϫ1). 72. Find an equation of the line passing through (5, 2) and the midpoint of the line segment joining (Ϫ1, 1) and (3, 9).

EXAMPLE 9 Sketch the graphs of a. 2x ϩ 3y Ϫ 6 ϭ 0 b. x Ϫ 3y ϭ 0 Solution a. Setting y ϭ 0 gives the x-intercept as 3. Next, setting x ϭ 0 gives the y-intercept as 2. Plotting the points (3, 0) and (0, 2) and drawing the line passing through them, we obtain the desired graph (see Figure 13a). b. Setting y ϭ 0 gives x ϭ 0 as the x-intercept. Next, setting x ϭ 0 gives y ϭ 0 as the y-intercept. Thus, the line passes through the origin. In this situation we need to find another point through which the line passes.