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Determine the infinite limit.

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

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$-\infty$ by (5)

03:03

Daniel Jaimes

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 2

The Limit of a Function

Limits

Derivatives

Missouri State University

Campbell University

Baylor University

University of Nottingham

Lectures

04:40

In mathematics, the limit of a function is the value that the function gets very close to as the input approaches some value. Thus, it is referred to as the function value or output value.

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

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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.

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