Limits and Derivatives#1

Limits and Derivatives#1 - 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) Motivation: Often, we are interested in finding the tangent to a curve. For example, we may want to find the instantaneous speed of a moving object, whose position is given by 2 ) ( t t s 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 L x f a x ) ( lim and say that “the limit of ) ( x f , as x approaches a , equals L if we can make the values of ) ( x f arbitrarily close to L by taking x to be sufficiently close to a (on either side of a ), but not equal to a .
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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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Limits and Derivatives#1 - MATH1010 Chapter 2 1 LIMITS AND...

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