Limits
"All of calculus is based on the idea of a limit. Not only are limits important in their own right but they also underlie the two fundamental operations of calculus: differentiation (calculating derivatives) and integration (evaluating integrals). Derivatives enable us to talk about the instantaneous rate of change of a function, which, in turn, leads to concepts such as velocity and acceleration, population growth rates, marginal cost, and flow rates. Integrals enable us to compute areas under curves, surface areas, and volumes. Because of the incredible reach of this single idea, it is essential to develop a solid understanding of limits. We first present limits intuitively by showing how they arise in computing instantaneous velocities and finding slopes of tangent lines. As the chapter progresses, we build more rigor into the definition of the limit and examine the different ways in which limits arise. The chapter concludes by introducing the important property of continuity and by giving the formal definition of a limit." (Briggs et al., 2019)
We will look at how to calculate limits later. For now, go the Integrals page, and let's look at how to calculate the volumes of solids.
"All of calculus is based on the idea of a limit. Not only are limits important in their own right but they also underlie the two fundamental operations of calculus: differentiation (calculating derivatives) and integration (evaluating integrals). Derivatives enable us to talk about the instantaneous rate of change of a function, which, in turn, leads to concepts such as velocity and acceleration, population growth rates, marginal cost, and flow rates. Integrals enable us to compute areas under curves, surface areas, and volumes. Because of the incredible reach of this single idea, it is essential to develop a solid understanding of limits. We first present limits intuitively by showing how they arise in computing instantaneous velocities and finding slopes of tangent lines. As the chapter progresses, we build more rigor into the definition of the limit and examine the different ways in which limits arise. The chapter concludes by introducing the important property of continuity and by giving the formal definition of a limit." (Briggs et al., 2019)
We will look at how to calculate limits later. For now, go the Integrals page, and let's look at how to calculate the volumes of solids.
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This website was prepared by Brant Breeding in his personal capacity. These materials are not endorsed, approved, sponsored, or provided by or on behalf of the University of Arkansas, Fayetteville.
Please follow this link for our full disclaimer statement.