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Problem 35 Medium Difficulty

Determine the infinite limit.

$ \displaystyle \lim_{x \to 3^+}\ln (x^2 - 9) $

Answer

$-\infty$ by (5)

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Video Transcript

we have a question and that's when they determine the infinite limit Yeah Limit X approaches do three from right side. Ellen Access Choir -9 We have recommend this. Okay. No the graphical method is the best matter for this. So if we suppose Y CUal to Ln access choir minus nine. If this is So to get the graph we have to first find the same tote a steamboat will be the next square -9 equal to zero. So X will be equal to Plus -3. So these are the same totes and since even power is there so it will be symmetrical curve or or even curve which is which will be symmetrical about the y axis. Okay for X and Y intercept for x intercept will be plugging in. Why call to zero which means Ln X esquire minus nine should be equal to zero which means Access choir -9 should be equal to one. So actually equal to 10. X should be called a plus minus under 10 which is 3.1 uh or 3.16. Anything export this is eccentricity and who I intercept will not be here Because there is there are symptoms at -1 and minus two anyhow for y intercept if we plug in X called 20 alan minus nine will be ah the output but negative of law. Rhythm is not possible. So let destroy it. This is X. This is why this is zero, This is UNDER 10. This is minus Under 10. Okay so And x equal to 3- and wrote 10 is -3.16. So actually equal to three will be somewhere here. X equal to -3, and X equal to three will be somewhere here. Okay. Who? So like this? And like this, they should be the what we say is and the graph of this Ellen X squared minus nine. Now, if we approach three from positive side from right side, if we are approaching three from right side that this is three from this side, if we are approaching this is three X equal to three. So this graph goes towards minus and 50. So its value will be well uh go to minus in finite, will approach to minus in finite. Thank you.