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March 14th, 2018, 03:42 AM   #1
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Does this limit equation have a solution?

Hello,

I ran through this limit question in the homework and I don't think it has a solution.

Can anyone figure out where the question is correct and has a solution or not.

I tried to simplify it but, I couldn't.



Last edited by wolfrose; March 14th, 2018 at 03:46 AM.
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March 14th, 2018, 04:05 AM   #2
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The limit is zero.
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March 14th, 2018, 05:08 AM   #3
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Wolfram Alpha describes it as the Laurent Series, with a limit at zero.
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March 14th, 2018, 06:54 AM   #4
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Could it simplified, as applying expansion rules to the numerator and denominator?

I tried to simplify the denominator to (x-1)(3x^2+x+1^2)

But couldn't simplify the numerator. Because there're no two numbers which can be multiplied to get -10 and the sum is +7!
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March 14th, 2018, 07:39 AM   #5
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[x^2 + 7x - 10] / [3x^3 - 1] = 0

Just looking at the equation:

if x^2 + 7x = 10, then you have a solution

3x^3 cannot equal 1
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March 14th, 2018, 07:41 AM   #6
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multiply numerator and denominator $x^{-3}$ ...

$\displaystyle \lim_{x \to \infty} \dfrac{\frac{1}{x} + \frac{7}{x^2} - \frac{10}{x^3}}{3 - \frac{1}{x^3}} = 0$

as $x \to \infty$ the value of each term in the numerator $\to 0$ and the value of the denominator $\to 3$
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March 14th, 2018, 07:51 AM   #7
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Quote:
Originally Posted by skeeter View Post


multiply numerator and denominator $x^{-3}$ ...

$\displaystyle \lim_{x \to \infty} \dfrac{\frac{1}{x} + \frac{7}{x^2} - \frac{10}{x^3}}{3 - \frac{1}{x^3}} = 0$

as $x \to \infty$ the value of each term in the numerator $\to 0$ and the value of the denominator $\to 3$
OK, so 0/3=0.

That's nice

Thanks, I thought any polynomial should be simplified by expansion rules or long division.

So, I can multiply anything with every part of the numerator and denominator by a factor to eliminate the high power on at the denominator.

Thank you,
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March 14th, 2018, 07:52 AM   #8
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Quote:
Originally Posted by Denis View Post

3x^3 cannot equal 1
Why? Is it because of the cubic power?
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March 14th, 2018, 08:43 AM   #9
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Because denominator would equal (1 - 1)
and dividing by 0 is a no-no !! Get it?
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March 14th, 2018, 10:08 AM   #10
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Yes, thank you
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