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 August 30th, 2016, 03:37 PM #1 Newbie   Joined: Aug 2016 From: LA Posts: 1 Thanks: 0 Is this true or false? Please explain also so I can learn. Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If lim x→c f(x) = L,then f(c) = L. a) False. If the limit of f as x approaches c is equal to L, then f(c) = cL. b) False. Define f to be the piece-wise function where f(x) = x + 3 when x ≠ −1 and f(x) = 2 when x = −1. Then we have that the limit of f as x approaches −1 is equal to −2, while f(−1) = 2. c) False. Define f to be the piece-wise function where f(x) = x − 4 when x ≠ 2 and f(x) = 0 when x = 2. Then we have that the limit of f as x approaches 2 is equal to −2, while f(2) = 0. D) False. If the limit of f as x approaches c is equal to L, then f(c) = L/c.
August 30th, 2016, 05:04 PM   #2
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All choices are false ... what does that tell you?

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 August 30th, 2016, 10:31 PM #3 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,671 Thanks: 2651 Math Focus: Mainly analysis and algebra What have you learned about limits? It makes a difference as to how it might be best explained. Clearly, the initial statement ($\lim \limits_{x \to c} f(x) = L \implies f(c)=L$) is false because all the options you give state that it is false. The question is, can you say why? I don't understand why anyone would pick answers a) and d), they don't sound anything like any part of the theory of limits as I understand it. One of b) and c) is correct, but if you have any understanding of limits it shouldn't be too difficult to decide which is correct. What do you think the answer should be, and why?
 September 1st, 2016, 02:43 PM #4 Senior Member   Joined: Aug 2016 From: morocco Posts: 273 Thanks: 32 If the function f is not continuous at x=c then limf(x) is not equal to f(c). x->c

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