Chapter 2 | Limits
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2.3 Estimate the area between the x -axis and the graph of f ( x ) = x 2 +1 over the interval [0, 3] by using the three rectangles shown here:
Other Aspects of Calculus So far, we have studied functions of one variable only. Such functions can be represented visually using graphs in two dimensions; however, there is no good reason to restrict our investigation to two dimensions. Suppose, for example, that instead of determining the velocity of an object moving along a coordinate axis, we want to determine the velocity of a rock fired from a catapult at a given time, or of an airplane moving in three dimensions. We might want to graph real-value functions of two variables or determine volumes of solids of the type shown in Figure 2.11 . These are only a few of the types of questions that can be asked and answered using multivariable calculus . Informally, multivariable calculus can be characterized as the study of the calculus of functions of two or more variables. However, before exploring these and other ideas, we must first lay a foundation for the study of calculus in one variable by exploring the concept of a limit.
Figure 2.11 We can use multivariable calculus to find the volume between a surface defined by a function of two variables and a plane.
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