Lecture-limits

Lecture-limits - MATH1010: Chapter 2 1 LIMITS AND...

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MATH1010: Chapter 2 1 LIMITS AND DERIVATIVES Now that we have an understanding of functions, we will move on to study limits of functions, which is the foundation of our future work with derivatives and integrals. Tangent/Velocity Problems (Section 2.1 of Stewart, pg. 83) One of the most important things that we are interested in is being able to find rates of change of functions! Suppose that the position of a moving object is given by 2 ) ( t t s = . If we were interested in finding it’s average rate of change over some period of time, that would be easy…just find the slope of the line joining two points. Question: How might we find the instantaneous rate of change (called the tangent to a curve) e.g. how quickly the object is moving at a particular instant of time? To find the slope of the tangent line, we can approximate this by the slope of the secant line , PQ , that goes through the point Q . If we try moving Q closer to P , first from the right, and then from the left, we obtain: x coord of Q mpq 23 1.5 2.5 1.1 2.1 1.01 2.01 1.001 2.001 and x coord of Q mpq 01 0.5 1.5 0.9 1.9 0.99 1.99 0.999 1.999 We say that m m pq P Q = lim
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MATH1010: Chapter 2 2 Limit of a Function (Section 2.2 of Stewart, pg. 88) Definition: We write
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This note was uploaded on 10/25/2011 for the course MATH 1010 taught by Professor Mihai during the Fall '08 term at UOIT.

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Lecture-limits - MATH1010: Chapter 2 1 LIMITS AND...

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