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Unformatted text preview: MIT OpenCourseWare http://ocw.mit.edu 18.01 Single Variable Calculus Fall 2006 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms . Lecture 2 18.01 Fall 2006 Lecture 2: Limits, Continuity, and Trigonometric Limits More about the rate of change interpretation of the derivative y = f(x) y x x y Figure 1: Graph of a generic function, with x and y marked on the graph 3. T temperature gradient y x dy dx as x Average rate of change Instantaneous rate of change Examples 1. q = charge dq dt = electrical current 2. s = distance ds dt = speed dT = temperature = dx 1 Lecture 2 18.01 Fall 2006 4. Sensitivity of measurements: An example is carried out on Problem Set 1. In GPS, radio signals give us h up to a certain measurement error (See Fig. 2 and Fig. 3). The question is L how accurately can we measure L . To decide, we find . In other words, these variables are h related to each other. We want to find how a change in one variable affects the other variable. L h s satellite you Figure 2: The Global Positioning System Problem (GPS) h s L Figure 3: On problem set 1, you will look at this simplified at earth model 2 Lecture 2 18.01 Fall 2006 Limits and Continuity...
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This note was uploaded on 10/28/2010 for the course CHAP 12 taught by Professor Lebec during the Spring '10 term at Marlboro.

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lec2 - MIT OpenCourseWare http://ocw.mit.edu 18.01 Single...

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