Infinite Limit vs Limits at Infinity of a Composite Function

Vertical asymptotes are (finite) values of x where limit of the function tends to either plus or minus infinity on one of the sides. Horizontal asymptotes look at whether the limit as x goes to plus or minute infinity approaches a finite value.

In this example we look at a tricky function that is a composition of e^(x) and a rational function. We find all vertical or horizontal asymptotes and use this to sketch a graph of the function

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Now it's your turn:
1) Summarize the big idea of this video in your own words
2) Write down anything you are unsure about to think about later
3) What questions for the future do you have? Where are we going with this content?
4) Can you come up with your own sample test problem on this material? Solve it!

Learning mathematics is best done by actually DOING mathematics. A video like this can only ever be a starting point. I might show you the basic ideas, definitions, formulas, and examples, but to truly master math means that you have to spend time - a lot of time! - sitting down and trying problems yourself, asking questions, and thinking about mathematics. So before you go on to the next video, pause and go THINK.

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Want more ideas for learning math effectively?
►How to Watch Math Videos:

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►Want some cool math? Check out my "Cool Math" Series:

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This video was created by Dr. Trefor Bazett, an Assistant Professor, Educator at the University of Cincinnati.

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[mehmetali]

you have the worst 2 on writing but you are perfect at teaching! great job thank you

[fardilviews]

Dr. I love your teaching... Love from Bangladesh

[hefestisllove]

Wait a minute, are you actually writing those down ? And if so, are you writing backwards ? And how ? It raises so many questions now that I have noticed it !

[franciscopen]

On your first example, x-3/x-2 is not defined for x approaching 2, so why did you go further to the e function approaching 2 if the inside function was not defined for 2?