Calculus Calculus Math Forum

 January 15th, 2018, 10:11 AM #1 Senior Member   Joined: May 2014 From: Allentown PA USA Posts: 113 Thanks: 6 Math Focus: dynamical systen theory A Proof concerning a negative f(x) Dear My Math Forum Community: What would be a suitable proof using the information below? Given: (1) the limit as x --> infinity, f(x)g(x) = L1 - L2 (2) the limit as x --> infinity, f(x) = L (3) L is finite Prove: the limit as x --> infinity, [ -f(x) ] = -L Thank you.  January 15th, 2018, 10:38 AM #2 Senior Member   Joined: Sep 2015 From: USA Posts: 2,638 Thanks: 1475 we are told that $\lim \limits_{x\to \infty} ~f(x) = L,~L \text{ is finite}$ $-1 \text{ is a finite constant}$ therefore by the constant law of limits $\lim \limits_{x \to \infty}~{-f(x)} = \lim \limits_{x \to \infty}~(-1) f(x) = (-1) \lim \limits_{x \to \infty}~ f(x) = (-1) L = -L$ January 15th, 2018, 11:02 AM #3 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,697 Thanks: 2681 Math Focus: Mainly analysis and algebra I assume there's an error in point 1) and that using $g(x)=-1$ gives the required result. January 20th, 2018, 10:17 AM   #4
Math Team

Joined: Jan 2015
From: Alabama

Posts: 3,264
Thanks: 902

Quote:
 Originally Posted by Carl James Mesaros Dear My Math Forum Community: What would be a suitable proof using the information below? Given: (1) the limit as x --> infinity, f(x)g(x) = L1 - L2
This makes no sense because you haven't said what L1 and L2 are! I suspect you mean that L1 is the limit of f(x) and L2 is the limit of g(x). But given that it should be lim f(x)g(x)= L1 times L2, not L1 minus L2.

Quote:
 (2) the limit as x --> infinity, f(x) = L (3) L is finite Prove: the limit as x --> infinity, [ -f(x) ] = -L Thank you.  Tags negative, proof Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Tau Math 40 December 31st, 2016 07:23 PM maxgeo Calculus 1 June 10th, 2014 02:48 PM daigo Algebra 3 June 30th, 2012 08:06 AM jstarks4444 Number Theory 11 February 17th, 2011 04:48 PM empiricus Algebra 6 May 4th, 2010 02:30 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top      