My Math Forum Is this true or false? Please explain also so I can learn.
 User Name Remember Me? Password

 Calculus Calculus Math Forum

 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
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.
Attached Images
 piecewise.jpg (7.7 KB, 11 views)

 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

,

,

,

### 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 Linear Mode

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

 Contact - Home - Forums - Cryptocurrency Forum - Top

Copyright © 2019 My Math Forum. All rights reserved.