# 1314L3 - Lesson 3 The Derivative The Limit Definition of...

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Lesson 3 – The Derivative 1 Lesson 3 The Derivative The Limit Definition of the Derivative We now address the first of the two questions of calculus, the tangent line question. We are interested in finding the slope of the tangent line at a specific point. We need a way to find the slope of the tangent line analytically for every problem that will be exact every time. We can draw a secant line across the curve, then take the coordinates of the two points on the curve, P and Q , and use the slope formula to approximate the slope of the tangent line. Consider this function:

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Lesson 3 – The Derivative 2 Now suppose we move point Q closer to point P . When we do this, we’ll get a better approximation of the slope of the tangent line. When we continue to move point Q even closer to point P , we get an even better approximation. We are letting the distance between P and Q get smaller and smaller. Now let’s give these two points names.
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## This note was uploaded on 02/15/2011 for the course MATH 1313 taught by Professor Constante during the Fall '08 term at University of Houston.

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1314L3 - Lesson 3 The Derivative The Limit Definition of...

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