My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum


Reply
 
LinkBack Thread Tools Display Modes
May 29th, 2018, 06:17 AM   #1
Member
 
Joined: Oct 2017
From: Japan

Posts: 62
Thanks: 3

How to solve limits (factoring)

Hi everyone,
if anyone is interested, here is a lesson on how to solve limits by factoring. Please let me know if you have any comment.
rudimt is offline  
 
May 29th, 2018, 07:08 AM   #2
Math Team
 
Joined: Jan 2015
From: Alabama

Posts: 3,261
Thanks: 894

Very good! I have just one comment. You refer to the quadratic $\displaystyle x^2+ 3x- 10$ as having roots -5 and 2 and so can be factored as $\displaystyle (x+ 5)(x- 2)$. I think it would be good to state that we know -5 is a root, and that x+ 5 is a factor, of $\displaystyle x^2+ 3x- 10$, because setting x= -5 made the numerator 0.
Country Boy is offline  
May 30th, 2018, 06:24 AM   #3
Member
 
Joined: Oct 2017
From: Japan

Posts: 62
Thanks: 3

Thank you! Even though how to solve quadratics is not the main focus I may indeed have mentioned it.
rudimt is offline  
May 30th, 2018, 10:15 AM   #4
Math Team
 
Joined: Jan 2015
From: Alabama

Posts: 3,261
Thanks: 894

My point is a bit more than that. If the numerator had been a cubic and we are looking at $\displaystyle \lim_{x\to 4}\frac{x^3- 4x^2+ 3x- 12}{x- 4}$ then setting x= 4, $\displaystyle \frac{4^3- 4(4^2)+ 3(4)- 12}{4- 4}= \frac{64- 65+ 12- 12}{4- 4}= \frac{0}{0}$.

My point is that the fact that the numerator is 0 when x= 4 tells us that x- 4 is a factor of the numerator. Since 12/4= 3, the factors must be $\displaystyle (x- 4)(x^2+ ax+ 3)= x^3+ ax^2+ 3x- 4x^2- 4ax- 12= x^3+ (a- 4)x^2+ (3- 4a)x- 12$. We must have a- 4= -4 and 3- 4a= 3. a= 0 satisfies both of those: $\displaystyle \frac{x^3- 4x^2+ 3x- 12}{x- 4}= \frac{(x- 4)(x^2- 3)}{x- 4}a$ which, for all x not equal to 4, is equal to $\displaystyle x^2- 3$. The limit, as x goes to 4, is 16- 3= 13.
Country Boy is offline  
Reply

  My Math Forum > College Math Forum > Calculus

Tags
factoring, limits, limitsfactoring, solve



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
please solve following limits??? ABHISHEK MEENA Calculus 5 December 28th, 2012 05:10 AM
Factoring stuff out of limits daigo Calculus 2 June 29th, 2012 03:53 AM
How to solve this limits ? shalikadm Calculus 4 May 31st, 2012 08:21 PM
solve by factoring help! oti5 Algebra 5 March 17th, 2012 11:59 AM
Solve Quadratic Equations by Factoring watkd Algebra 18 September 6th, 2010 01:34 PM





Copyright © 2018 My Math Forum. All rights reserved.