May 17th, 2017, 10:38 AM  #1 
Member Joined: May 2014 From: Allentown PA USA Posts: 87 Thanks: 6 Math Focus: dynamical systen theory  problem with a calculus exercise
Dear MyMathForum Community: I tried understanding this problem, but to no avail. Find an appropriate number L, and a deleted neighborhood N of a, such that given k > 0, L  k < f(x) < L + k here, f(x) = 4/x, and a = 2. The correct answer to this exercise is: 0 < abs(x2) < 2k/(2  k). I cannot understand how the author got this answer. Thank you. Best regards, Carl Mesaros Last edited by skipjack; May 18th, 2017 at 05:06 AM. 
May 19th, 2017, 10:25 AM  #2 
Member Joined: Jan 2016 From: Athens, OH Posts: 40 Thanks: 24 
You didn't state the problem very well. Since this is calculus, I assume you mean: for a=2, L=2 and for any k>0, find $\delta>0$ such that for any x with $0<x2<\delta$, it follows that $4/x2<k$. Whoever gave the solution $\delta=2k/(2k)$ is incompetent (I hope not the author of the text). First if $k>2$, $\delta$ isn't even positive. Here's how the incorrect $\delta$ was found: Solve $${4\over2+\delta}=2k\text{ for }\delta$$ For this particular function, you can solve $${4\over 2\delta_1}=2+k\text{ for }\delta_1$$ Then a correct deleted neighborhood is $(2\delta_1,2+\delta)\setminus \{2\}$ The only reason this works is that the function is decreasing, so it is not a general good procedure. Here's a graph that shows that $\delta$ is wrong: 
May 22nd, 2017, 01:53 AM  #3 
Member Joined: May 2014 From: Allentown PA USA Posts: 87 Thanks: 6 Math Focus: dynamical systen theory  An apology
Dear Johng40: You are right. I did not state the problem correctly. My apologies I offer to you. The basic problem I had is how to manipulate 4/x in a way that would make the solution of the problem possible. Thank you. Best regards, Carl Mesaros 

Tags 
calculus, exercise, problem 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
exercise problem IEEE 754 floating point  abdel  Computer Science  3  October 22nd, 2012 05:28 AM 
Calculus New problem  mathkid  Calculus  6  September 5th, 2012 09:19 AM 
Calculus big problem 3  Aliano9  Calculus  1  December 9th, 2009 05:21 AM 
Calculus problem.  ZardoZ  Calculus  4  January 1st, 1970 12:00 AM 
Calculus problem  listolad  Calculus  1  January 1st, 1970 12:00 AM 