By Robert Smith, Roland Minton

Now in its 4th variation, Smith/Minton, Calculus bargains scholars and teachers a mathematically sound textual content, powerful workout units and stylish presentation of calculus thoughts. whilst packaged with ALEKS Prep for Calculus, the best remediation instrument out there, Smith/Minton deals a whole package deal to make sure scholars good fortune in calculus. the hot version has been up to date with a reorganization of the workout units, making the variety of routines extra obvious. also, over 1,000 new vintage calculus difficulties have been further.

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**Additional info for Calculus, 4th Edition **

**Sample text**

Perpendicular lines Solution We began this section by showing that the points in the corresponding table are not colinear. Nonetheless, they are nearly colinear. So, why not use the straight line connecting the last two points (20, 227) and (30, 249) (corresponding to the populations in the years 1980 and 1990) to predict the population in 2000? ) The slope of the line joining the two data points is y 300 200 m= 100 22 11 249 − 227 = = . 20 11 (x − 30) + 249. 20 for a graph of the line. If we follow this line to the point corresponding to x = 40 (the year 2000), we have the predicted population Population 11 (40 − 30) + 249 = 271.

To determine whether the points are, in fact, on the same line (such points are called colinear), we might consider the population growth in each of the indicated decades. From 1960 to 1970, the growth was 24 million. ) Likewise, from 1970 to 1980, the growth was 24 million. However, from 1980 to 1990, the growth was only 22 million. Since the rate of growth is not constant, the data points do not fall on a line. This argument involves the familiar concept of slope. y 10 Lines and Functions LINES AND FUNCTIONS Year 1960 1970 1980 x ..

Further, any two vertical lines are parallel. , m 1 · m 2 = −1). Also, any vertical line and any horizontal line are perpendicular. Since we can read the slope from the equation of a line, it’s a simple matter to determine when two lines are parallel or perpendicular. 6. cls 12 .. 5 20 Finding the Equation of a Parallel Line Find an equation of the line parallel to y = 3x − 2 and through the point (−1, 3). Solution It’s easy to read the slope of the line from the equation: m = 3. The equation of the parallel line is then 10 Ϫ4 T1: OSO December 8, 2010 x Ϫ2 2 y = 3[x − (−1)] + 3 4 or simply y = 3x + 6.