Chap2_Sec2

Chap2_Sec2 - THE LIMIT OF A FUNCTION Guess the value of...

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2 1 1 lim 1 x x x THE LIMIT OF A FUNCTION Example 1 (2.2) Guess the value of . ± Is f(x) defined when x = 1? ± Does this affect the limit of f(x) as x approaches 1?
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The tables give values of f ( x ) (correct to six decimal places) for values of x that approach 1 (but are not equal to 1). ± What is ? THE LIMIT OF A FUNCTION Example 1
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Example 1 is illustrated by the graph of f in the figure. THE LIMIT OF A FUNCTION Example 1
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Now, let’s change f slightly by giving it the value 2 when x = 1 and calling the resulting function g : () 2 1 1 1 21 x if x gx x if x = = THE LIMIT OF A FUNCTION Example 1
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This new function g still has the same limit as x approaches 1. THE LIMIT OF A FUNCTION Example 1
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Investigate . ± Is f ( x ) defined at 0? ± Does it affect the limit of f(x) as x approaches 0? 0 limsin x x π THE LIMIT OF A FUNCTION Example 4 (2.2)
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Evaluating the function for some small values of x , we get: Similarly, f (0.001) = f (0.0001) = 0.
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This note was uploaded on 05/23/2011 for the course MAC 2311 taught by Professor Noohi during the Fall '08 term at FSU.

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Chap2_Sec2 - THE LIMIT OF A FUNCTION Guess the value of...

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