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Numerade Educator

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Problem 12 Medium Difficulty

Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consider using it. If l'Hospital's Rule doesn't apply, explain why.

$ \displaystyle \lim_{x\to 1/2} \frac{6x^2 + 5x - 4}{4x^2 + 16x - 9} $

Answer

11/ 20

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Video Transcript

So for this probably want to factor the numerator first and then simplify. So when we factor the numerator It will be three x plots four Times two X -1. Yeah. Provided by two X plus nine Times to Act -1. Yes. Based on this it's clear that the two x minus ones can cancel leaving us with just three X plus 4/2 X plus nine. Then when you plug in the one half that would end up giving us 11 which would be our final answer, another option would need to use low petals role to take the derivative of the top and bottom. Doing that would also give us 11/20. And that's because we would get 12 x plus five divided by eight X. Class 16. And we see here that if we plugged in in this case we plugged in X equals um one half. We would end up getting right here .55 as well.