May 8th, 2013, 11:25 AM  #1 
Newbie Joined: May 2013 Posts: 3 Thanks: 0  limit statements true or not?
which of the following statements MUST be true, MIGHT be true, or is NEVER true about a function f which is defined for all real numbers? Justify your answer. a) lim x>a f(x)=f(a) might be true if this is a continuous function b)If lim x> f(x)/x=1 then lim x>0 f(x)=0 
May 8th, 2013, 11:31 AM  #2 
Newbie Joined: May 2013 Posts: 3 Thanks: 0  Re: limit statements true or not?
and also c) If the average rate of change of a function between two points is zero, then the function is constant between those two points.

May 8th, 2013, 12:37 PM  #3 
Senior Member Joined: Feb 2012 Posts: 628 Thanks: 1  Re: limit statements true or not?
Statement A must be true, because if it was not true, then there would be a discontinuity at x = a. Statement B is unclear. (The limit as x approaches what value of f(x)/x?) Statement C might be true, although it probably isn't. The average rate of change on an interval (a, b) is just , which is 0 if , but this alone does not guarantee that for every point c between a and b. 
May 8th, 2013, 12:55 PM  #4  
Newbie Joined: May 2013 Posts: 3 Thanks: 0  Re: limit statements true or not? Quote:
 
May 10th, 2013, 08:35 AM  #5 
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  Re: limit statements true or not?
If the numerator of a fraction goes to 0 and the denominator does not what happens to the fraction?


Tags 
limit, statements, true 
Search tags for this page 
which of the following statments must be true, might be true or is never true about a function f which is defined for all real numbers? justify your answer. if lim as x approaches 0 of f(x)/x =1, then f(0)=0,which of the following must be true might be true or is never true about a function
Click on a term to search for related topics.

Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Which statements are true?  jblaven  Applied Math  8  February 5th, 2014 02:20 PM 
limit true false question  xdeimos99  Real Analysis  1  October 17th, 2013 11:47 PM 
Limit statements  layd33foxx  Calculus  8  September 26th, 2011 01:14 PM 
Proving limit statements Xsin1/X  oddlogic  Calculus  2  January 25th, 2010 02:04 PM 
Set Statements  jstarks4444  Number Theory  2  December 31st, 1969 04:00 PM 