November 3rd, 2018, 07:34 AM  #1 
Newbie Joined: Sep 2018 From: Spain Posts: 11 Thanks: 0 
Hi I need to answer the following equation: $\displaystyle \lim_{x\to2}$ (x³ + 3x  1) = x3 = x to the power of 3 Last edited by skipjack; November 3rd, 2018 at 10:37 AM. 
November 3rd, 2018, 09:51 AM  #2 
Senior Member Joined: May 2016 From: USA Posts: 1,310 Thanks: 550 
Show x to the power of 3 as x^3. One way to answer this question is to use the laws of limits. $\displaystyle \lim_{x \rightarrow a} f(x) = b, \ \lim_{x \rightarrow a} g(x) = c, \text { and } h(x) = f(x) + g(x) \implies \lim_{x \rightarrow a} h(x) = b + c.$ $\displaystyle \lim_{x \rightarrow a} f(x) = b, \ \lim_{x \rightarrow a} g(x) = c, \text { and } h(x) = f(x)  g(x) \implies \lim_{x \rightarrow a} h(x) = b  c.$ $\displaystyle \lim_{x \rightarrow a} f(x) = b, \ \lim_{x \rightarrow a} g(x) = c, \text { and } h(x) = f(x) * g(x) \implies \lim_{x \rightarrow a} h(x) = bc.$ $\displaystyle \lim_{x \rightarrow a} f(x) = b, \ \lim_{x \rightarrow a} g(x) = c, \ c \ne 0, \text { and } h(x) = \dfrac{f(x)}{g(x)} \implies \lim_{x \rightarrow a} h(x) = \dfrac{b}{c}.$ 
November 3rd, 2018, 10:06 AM  #3 
Newbie Joined: Sep 2018 From: Spain Posts: 11 Thanks: 0 
Okay, so what's the answer?
Last edited by skipjack; November 3rd, 2018 at 10:39 AM. 
November 3rd, 2018, 10:38 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 20,390 Thanks: 2015 
What do you get by replacing each "x" in "x³ + 3x  1" with "2" and evaluating the result?

November 3rd, 2018, 11:50 AM  #5 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,623 Thanks: 2611 Math Focus: Mainly analysis and algebra  
November 3rd, 2018, 12:59 PM  #6 
Banned Camp Joined: Mar 2015 From: New Jersey Posts: 1,720 Thanks: 125 
Informally, substitute x = 2 Formally, limit of a sum is sum of its summands limits, and limit of a product is product of its factors limits. limit x = 2. 
November 3rd, 2018, 01:32 PM  #7 
Senior Member Joined: Sep 2016 From: USA Posts: 579 Thanks: 345 Math Focus: Dynamical systems, analytic function theory, numerics  
November 4th, 2018, 02:23 AM  #8 
Newbie Joined: Sep 2018 From: Spain Posts: 11 Thanks: 0  
November 4th, 2018, 02:57 AM  #9 
Senior Member Joined: Oct 2009 Posts: 753 Thanks: 261  
November 4th, 2018, 04:35 AM  #10 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,623 Thanks: 2611 Math Focus: Mainly analysis and algebra 
He is clearly clever enough that he doesn't need any help.


Tags 
limits 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
limits  consigliere  Calculus  4  January 30th, 2013 05:54 AM 
Limits 2  math89  Calculus  2  January 26th, 2013 04:11 PM 
Limits  Arley  Calculus  2  April 2nd, 2012 05:50 PM 
Limits,Finding functions by limits  kadmany  Calculus  9  March 18th, 2011 06:16 AM 
Limits  lilwayne  Calculus  18  September 23rd, 2010 02:39 PM 