Another question about limits

[Kerr]

Hi all.

Could anyone explain the best way to calculate these two limits?

I basically know their value, partly due to guesses, "ugly tricks" and mathematica. Like I can do like this:

But that feels really dirty since I am doing multiplication and addition with negative infinity, which my brain regards as an undefined operation and, as such, not correct math.

How do you solve problems like this in a proper way?

Take care,
Kerr.

 

[freethinker44]

There are a lot of different ways to find limits depending on what type of function you are using.

Khan Academy is a good resource for learning calculus. My college calculus instructor even uses their videos as a teaching aid.

 

[Kerr]

There are a lot of different ways to find limits depending on what type of function you are using.

Khan Academy is a good resource for learning calculus. My college calculus instructor even uses their videos as a teaching aid.

Thanks . Will take a look.

Another question, though. Had an idea earlier. One of the issues I have is keeping track of all the factors when there are too many of them. It confuses my brain. So, one way to solve that could be use variable substitution and define t = e^x. When x -> 0 then t -> 1. So then I could rewrite

into

,
which would make it easier for me to solve.

Would that bad math or wrong in some way?