Lesson 3-filled-b - Math 1314 Lesson 3 The Derivative The...

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Math 1314 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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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. Suppose we 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. What does this sound like?
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Now let’s give these two points names. We’ll express them as ordered pairs. Now we’ll apply the slope formula to these two points.
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Lesson 3-filled-b - Math 1314 Lesson 3 The Derivative The...

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