Help about limits, please
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Help about limits, please

[From: ] [author: ] [Date: 11-05-22] [Hit: ]
..its equal zero so we have to resolve by factoring..........
What is the limit of: (3x²+2x-1)/(9x²-1) when x->1/3?

The answer is 2/3 but it doesn't the same result i did

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Start out by factoring the numerator and denominator to get:
(a) 3x^2 + 2x - 1 = (3x - 1)(x + 1)
(b) 9x^2 - 1 = (3x + 1)(3x - 1).

So, we have:
lim (x-->1/3) (3x^2 + 2x - 1)/(9x^2 - 1)
= lim (x-->1/3) [(3x - 1)(x + 1)]/[(3x + 1)(3x - 1)], by factoring
= lim (x-->1/3) (x + 1)/(3x + 1), by canceling 3x - 1
= (1/3 + 1)/(1 + 1)
= 2/3, as required.

I hope this helps!

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rewrite: (x+1)/(3 x+1)
plug in x=1/3

answer=2/3

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lim x->1/3 (3x² + 2x - 1)/(9x² - 1)

= lim x->1/3 (3x - 1)(x + 1)/(3x + 1)(3x - 1) = lim x->1/3 (x + 1)/(3x + 1) = (4/3)/(2) = 2/3

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Hmm...it's equal zero so we have to resolve by factoring....
1
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