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Applying this reasoning to the problem with c 2 we

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and the two are equal. Applying this reasoning to the problem, with c = 2 , we see that lim x 2 + f ( x ) = 7 . Note, that we cannot say anything about lim x 2 f ( x ) without knowing more about the function f . For example, it could be the case that for values x < 2 and x > 2 , f is not defined, in which case the statement lim x 2 f ( x ) does not make sense. For another example, it could also be the case the f ( x ) = 7 for all real numbers x , in which case lim x 2 f ( x ) = 7 . In short, it is impossible to comment on this limit from the information given.

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Math 1110 (Fall 2011) HW3 Presentation Problems 3 Question 3. (7 points) Consider the function f ( x ) graphed in the figure below. x=0 y=0 y=1 x=1 (a) For what values c is lim x c + f ( x ) = 2 ? We want to find the x -coordinate for points on the graph where the right-hand limit equals 2. These are c = 3 , c = 0 , and c = 2 . Since it is difficult to see exactly what is happening in the graph near the point ( 2, 2 ) , another acceptable answer would be c = 3 , c = 0 , c = 2 , and c 2.2 .
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• Fall '06
• MARTIN,C.
• Calculus, Limit, Continuous function

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