RedAssign1[1].2 - the answer represented by the derivative...

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Unit: Introduction to Calculus II Module: Introduction Calculus I in 20 Minutes [email protected] Copyright 2001, Thinkwell Corp. All Rights Reserved. 1547 –rev 06/13/2001 Calculus accomplishes two goals: determining instantaneous rates of change and calculating the area under a curve. The derivative is a function that gives the slope of the line tangent to a given function at any point. It is the basis of differential calculus and it is used to determine instantaneous rates. An integral “undoes” a derivative to produce the original function. Integral calculus reverses differential calculus and determines the area under a curve. Calculus asks the question “What is the instantaneous rate of change?” To answer this question, you need to think of instantaneous rate of change as the slope of a tangent line. Calculating the slope leads to an indeterminate form . By taking a limit and using algebraic tricks you arrive at
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Unformatted text preview: the answer, represented by the derivative . To take the derivative of a complicated function you may need to use the product rule , the quotient rule or the chain rule . Implicit differentiation will allow you to take derivatives of relations. Derivatives are useful for answering questions about velocity and acceleration, linear approximation, maxima and minima, and related rates. The first and second derivatives are also useful when graphing functions. Integral calculus begins by finding a function that corresponds to a given derivative. These are called antiderivatives , which lead to integrals . A technique that will help you integrate some functions is u-substitution , which reverses the chain rule. Integrals are useful for determining velocity and position when given acceleration. The second question that calculus asks, “What is the area under a curve?” is answered by the fundamental theorem of calculus ....
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This note was uploaded on 04/27/2010 for the course MATH 172 taught by Professor Hyon during the Spring '10 term at Community College of Denver.

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