Limits confusion

[Dr.Peterson]

It's how it was written to the board. The student might have done it wrong without professor noticing. I don't know, I wasn't there at the time.

So when you said "my professor used the second approach", you really meant that a student wrote this in class, and the professor, to your knowledge, did not correct it, but the whole thing is a second-hand report because you were not there. Ignore it!

Do you perhaps know of any videos (like khan academy or similar) when they take a function, find asymptotes, determine min and max y values and etc... I am really confused by this.

This topic (commonly taught before calculus) can be found by searching for "graphing rational functions". (The min and max will use calculus, but that is no different from any other max/min problem.)

 

[JeffM]

Why use such method when you have l'Hospital?

Because this was posted in algebra, it is quite possible that the student does not even know differentiation, let alone L'Hospital.

Indeed, it is possible that the student does not have a formal grasp of limits.

I think what is being taught is an informal but intuitive way to find asymptotes.

 

[Loki123]

Why use such method when you have l'Hospital?

While it would be easier i'd like to know other methods.

 

[BigBeachBanana]

While it would be easier i'd like to know other methods.

For polynomials, you simply have to compare the highest power of the numerator and denominator. Essentially, that's l'Hospital. That's not easy enough?

 

[JeffM]

While it would be easier i'd like to know other methods.

To apply in full generality, it requires differential calculus. As BBB says, in the case of rational functions, it reduces to a rule based on the degrees of the polynomials in the numerator and denominator.