Work with functions represented in a variety of ways: graphical, numerical, analytical, or verbal. You should understand the connections among these representations. Understand the meaning of the derivative in terms of a rate of change and local linear approximation and use derivatives to solve a variety of problems. Understand the meaning of the definite integral both as a limit of Riemann sums and as the net accumulation of change and use integrals to solve a variety of problems. Understand the relationship between the derivative and the definite integral as expressed in both parts of the Fundamental Theorem of Calculus. Communicate mathematics both orally and in well-written sentences and explain solutions to problems. Model a written description of a physical situation with a function, a differential equation, or an integral. Use technology to help solve problems, experiment, interpret results, and verify conclusions. Determine the reasonableness of solutions, including sign, size, relative accuracy, and units of measurement. Develop an appreciation of calculus as a coherent body of knowledge and as a human accomplishment.
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