limits_adj - ECON1003 Mathematics for the Social Sciences...

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1 ECON1003 Mathematics for the Social Sciences Topic 7: Limits and Continuity Lecturer: Marlon Tracey
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2 Objective o At the end of this topic, students should be able to: o Define the limit of a function. o Compute the limits of polynomial and rational functions. o Compute one-sided limits and limits to infinity of a function. o Determine the continuity and/or discontinuity of a function.
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3 Outline o Defining a limit o Limit of polynomials and rational functions o Limit to infinity o One-sided Limits o Continuity o Points of discontinuity
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Defining a limit I Conclusion : As x gets closer and closer to 3, whether from the right (+) or the left (-), f(x) will approach a value of 10. x f(x) = 2x+4 2.999 9.998 2.99 9.98 2.9 9.8 4 x gets closer to 3 f(x) gets closer and closer to 10 10 ) ( lim 3 = - x f x x f(x) = 2x+4 3.001 10.002 3.01 10.02 3.1 10.2 x gets closer to 3 f(x) gets closer and closer to 10 10 ) ( lim 3 = + x f x 10 ) ( lim 3 = x f x
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5 Defining a limit II o Formally then, a limit examines what happens to a function f(x) as x gets closer and closer to a particular value c. o
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This note was uploaded on 03/16/2011 for the course ECON 1003 taught by Professor Dr.mcdonald during the Spring '11 term at University of the West Indies at Mona.

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limits_adj - ECON1003 Mathematics for the Social Sciences...

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