My Math Forum Limit of x --> +1

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 March 15th, 2017, 04:56 AM #1 Newbie   Joined: Mar 2017 From: Norway Posts: 4 Thanks: 0 Limit of x --> +1 Hi, I am a new member in here. My daughter has asked me this question and after I solved it she was not agree with my solution. Can anyone help me with the correct solution please? Here is the problem: If (3x² + ax)=a+2 lim x --> +1 Find values of "a" And here is what I did: [3(1.1)²+ a(1.1)]= a+2 a+2<=3.6+a.a= -16 a< -6
 March 15th, 2017, 06:27 AM #2 Math Team   Joined: Dec 2013 From: Colombia Posts: 6,876 Thanks: 2240 Math Focus: Mainly analysis and algebra I can't make sense of the question, but if there is a limit to be obtained as $x \to 1$ then making $a$ the subject of the equation and finding the limit as $x \to 1$ would seem sensible. But the limit exists only if the $2$ in the question should be a $3$, in which case I get $a=-6$. Last edited by v8archie; March 15th, 2017 at 06:36 AM.
 March 15th, 2017, 07:26 AM #3 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,541 Thanks: 921 Math Focus: Elementary mathematics and beyond First of all, $3x^2+ax$ is a polynomial so there's no reason that direct substitution cannot be used. That gives us $3+a=a+2$, which is absurd. I'm assuming $x$ and $a$ are real.
March 15th, 2017, 09:24 AM   #4
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Quote:
 Originally Posted by v8archie I can't make sense of the question, but if there is a limit to be obtained as $x \to 1$ then making $a$ the subject of the equation and finding the limit as $x \to 1$ would seem sensible. But the limit exists only if the $2$ in the question should be a $3$, in which case I get $a=-6$.
Thank you very much for your explanation.
I really appreciate it if you could show me how to get $a=-6$ and why that is the only value for $a$.

 March 15th, 2017, 10:09 AM #5 Math Team   Joined: Dec 2013 From: Colombia Posts: 6,876 Thanks: 2240 Math Focus: Mainly analysis and algebra Perhaps you could write down the full question first.
March 15th, 2017, 10:20 AM   #6
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Quote:
 Originally Posted by v8archie Perhaps you could write down the full question first.
This is the exact wording of the problem:

If (3x² + ax)=a+2
lim x --> +1

Find values of "a"

March 15th, 2017, 11:21 AM   #7
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Quote:
 Originally Posted by Farzin This is the exact wording of the problem: If (3x² + ax)=a+2 lim x --> +1 Find values of "a"
If that is the problem, it contains one or more typographical errors. There is no such number. Full stop.

March 15th, 2017, 11:25 AM   #8
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 Originally Posted by JeffM1 If that is the problem, it contains one or more typographical errors. There is no such number. Full stop.
Thank you very much.

 March 15th, 2017, 02:46 PM #9 Math Team   Joined: Dec 2013 From: Colombia Posts: 6,876 Thanks: 2240 Math Focus: Mainly analysis and algebra If, as I suggested above the question were $3x^2 + ax=a+3$, this can be rearranged (when $x\ne 1$) to get $$a=-\frac{3x^2-3}{x-1}=-\frac{3(x+1)\cancel{(x-1)}}{\cancel{(x-1)}}=-3(x+1)$$ Taking the limit of this expression as $x \to 1$ gives $a=-6$ Thanks from greg1313 and topsquark

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