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Intuition before Formality. Calculus & Its Applications builds intuition with key concepts of calculus before the analytical material. For example, the authors explain the derivative geometrically before they present limits, and they introduce the definite integral intuitively via the notion of net change before they discuss Riemann sums. The strategic organization of topics makes it easy to adjust the level of theoretical material covered. The significant applications introduced early in the course serve to motivate students and make the mathematics more accessible. Another unique aspect of the text is its intuitive use of differential equations to model a variety of phenomena in Chapter 5, which addresses applications of exponential and logarithmic functions.

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Given information: Set of real numbers, rational numbers, and irrational numbers Explanation:...Given information: Non-vertical line Explanation: The slope of a non-vertical line is the rate of...Given information: Describe all the important terms from the graph of functions. Explanation: There...Given information: Instructions to describe the product rule and the quotient rule. Explanation: If...Given information: Instruction to describe thelaws of exponents. Explanation: The function f ( x ) =...Given information: The instruction to state the differential equation which is the key to solve the...Given information: Instruction to state the meaning of anti-differentiate a function. Explanation:...Given information: Instruction to state an example of a level curve of a function of two variables...Given information: Instruction to state the radian measure of an angle Explanation: To define a...

Given information: Instructions to describe integration by substitution Explanation: If f(x) and...Given information: Instruction to describe the meaning of a differential equation Explanation: A...Given information: Instruction to describe the n th Taylor polynomial of f(x) at x = a. Explanation:...Given information: Instruction to explain the probability table Explanation: An experiment consists...

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