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 October 25th, 2009, 06:11 PM #1 Newbie   Joined: Oct 2009 Posts: 4 Thanks: 0 Find a value a such that limit lim ((5x^2+ax+/(x^2-x-2)) x->2 How do I find the value of a? Could someone help me with this problem? Thank you
 October 25th, 2009, 06:16 PM #2 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,807 Thanks: 1045 Math Focus: Elementary mathematics and beyond Re: Find a value a such that limit What is $\lim_{x \to 2}\,\frac{5x^2\,+\,ax\,+\,8}{x^2\,-\,x\,-\,2}$ equal to?
October 25th, 2009, 06:27 PM   #3
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Re: Find a value a such that limit

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 Originally Posted by greg1313 What is $\lim_{x \to 2}\,\frac{5x^2\,+\,ax\,+\,8}{x^2\,-\,x\,-\,2}$ equal to?
That's the only question it has. There is no equal. It ask me to find the value of a of that limit, and then find the limit.

 October 25th, 2009, 06:33 PM #4 Senior Member   Joined: Mar 2007 Posts: 428 Thanks: 0 Re: Find a value a such that limit You can perform the division, or factor and consider that you'd need to reduce by the factor(x - 2), or can use the Factor Theorem to show that the top is divisible by the bottom [has a remainder of zero] if a = -14 giving a limiting value of 2. Otherwise the denominator approaches zero.
October 25th, 2009, 06:47 PM   #5
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Re: Find a value a such that limit

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 Originally Posted by David You can perform the division, or factor and consider that you'd need to reduce by the factor(x - 2), or can use the Factor Theorem to show that the top is divisible by the bottom [has a remainder of zero] if a = -14 giving a limiting value of 2. Otherwise the denominator approaches zero.
you said that the denominator approaches zero, so the a will be 0 too. Am I right?

 October 25th, 2009, 07:24 PM #6 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,807 Thanks: 1045 Math Focus: Elementary mathematics and beyond Re: Find a value a such that limit As David pointed out, the a is -14. $\lim_{x \to 2}\,\frac{(x\,-\,2)(5x\,-\,4)}{(x\,-\,2)(x\,+\,1)}\,=\,\lim_{x \to 2}\,\frac{5x\,-\,4}{x\,+\,1}\,=\,2$ $(5x\,-\,4)(x\,-\,2)=5x^{2}\,-\,14x\,+\,8$
 October 25th, 2009, 08:39 PM #7 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,807 Thanks: 1045 Math Focus: Elementary mathematics and beyond Re: Find a value a such that limit "Find a value a such that [the] limit [exists]" ?
 October 25th, 2009, 08:59 PM #8 Newbie   Joined: Oct 2009 Posts: 1 Thanks: 0 Find a value a such that limit LIM x->2 sin(1/x-1/2) can anybody solve this problem?
October 26th, 2009, 06:13 AM   #9
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Re: Find a value a such that limit

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 Originally Posted by greg1313 As David pointed out, the a is -14. $\lim_{x \to 2}\,\frac{(x\,-\,2)(5x\,-\,4)}{(x\,-\,2)(x\,+\,1)}\,=\,\lim_{x \to 2}\,\frac{5x\,-\,4}{x\,+\,1}\,=\,2$ $(5x\,-\,4)(x\,-\,2)=5x^{2}\,-\,14x\,+\,8$
Yes, but I tried not to do it for him.

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