November 3rd, 2018, 08:34 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 11:37 AM. 
November 3rd, 2018, 10:51 AM  #2 
Senior Member Joined: May 2016 From: USA Posts: 1,192 Thanks: 489 
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, 11:06 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 11:39 AM. 
November 3rd, 2018, 11:38 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 19,878 Thanks: 1835 
What do you get by replacing each "x" in "x³ + 3x  1" with "2" and evaluating the result?

November 3rd, 2018, 12:50 PM  #5 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,502 Thanks: 2511 Math Focus: Mainly analysis and algebra  
November 3rd, 2018, 01:59 PM  #6 
Senior Member Joined: Mar 2015 From: New Jersey Posts: 1,603 Thanks: 115 
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, 02:32 PM  #7 
Senior Member Joined: Sep 2016 From: USA Posts: 503 Thanks: 281 Math Focus: Dynamical systems, analytic function theory, numerics  
November 4th, 2018, 03:23 AM  #8 
Newbie Joined: Sep 2018 From: Spain Posts: 11 Thanks: 0  
November 4th, 2018, 03:57 AM  #9 
Senior Member Joined: Oct 2009 Posts: 610 Thanks: 187  
November 4th, 2018, 05:35 AM  #10 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,502 Thanks: 2511 Math Focus: Mainly analysis and algebra 
He is clearly clever enough that he doesn't need any help.


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