
Calculus Calculus Math Forum 
 LinkBack  Thread Tools  Display Modes 
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 piecewise 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 piecewise 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 
Math Team Joined: Jul 2011 From: Texas Posts: 2,982 Thanks: 1575 
All choices are false ... what does that tell you? Correct response is depicted in the attached graph. 
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 

Tags 
explain, false, learn, true 
Search tags for this page 
if lim f(x)=l then f(c)=l,F.YT..JPixiesic.' i., . .............,........ji g, s ........Fl.X.iferff.....v......,. Spl.p . .f....c'l,the limit of f(x) as x approas 1 is equal to 1, is true or false?,determine whether the statement is true or false. if it is false give an example
Click on a term to search for related topics.

Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
True or False  Taliaferro  Calculus  6  August 7th, 2014 05:41 PM 
true or false  outsos  Abstract Algebra  5  April 4th, 2012 11:56 AM 
true and false .?  sam_17  Abstract Algebra  12  March 29th, 2012 02:27 PM 
true or false???  shimaa  Calculus  1  February 17th, 2012 11:45 AM 
True or False and WHY?  bradycat  Algebra  2  January 31st, 2009 07:28 AM 