Thomas calculus 12th edition solution manual chapter 1-9
If we first make a scatterplot and then connect approximately the data points (t, p) from the table, we obtain the graph shown in Figure 1.6. The table provides a representation of the pressure function over time. The data in Table l.l give recorded pressure displacement versus time in seconds of a musical note produced by a toning fork. The graph consisting of only the points in the table is called a scatterplot.ĮXAMPLE 3 Musical notes are pressure waves in the air. From an appropriate table of values, a graph of the function can be obtained using the method illustrated in Example 2, possibly with the aid of a computer. Numerical representations are often used by engineers and scientists. Another way to represent a function is numerically, through a table of values. Representing a Function Numerically We have seen how a function may be represented algebraically by a formula (the area function) and visually by a graph (Example 2).
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Meanwhile we will have to settle for plotting points and connecting them as best we can. But how would we then connect them? The basic question still remains: How do we know for sure what the graph looks like between the points we plot? Calculus answers this question, as we will see in Chapter 4. How do we know that the graph of y = x 2 doesn't look like one of these curves? (2.4)
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