Question

We're learning L'Hospital's rule, and I don't understand how or why you would plug in infinity and negative infinity for certain things? And do I need to know parent graphs?

Answer 1

you don't really "plug them in" you eyeball the limit
you got an example?

Answer 2

Yup! Here's one from our notes:
x approaches 0+ sinx/x^2

One from the homework I'm not sure on is:
x approaches infinity (1/x -1/(e^x-1))

Answer 3

You could take the limit (as x approaches infinity) of each of those two terms separately, and then combine the resulting limits.

What is the limit (as x approaches infinity) of 1/x?
What is the limit (as x approaches infinity) of 1/(e^(x-1)?

I've just realized that there's ambiguity here.

In the expression e^x-1, did you mean e^(x-1) or did you mean (e^x) - 1? Those parentheses can make a huge difference. Err on the side of using too many parentheses, rather too few.

Answer 4

And note that I used one too few parenthesis in typing 1/(e^(x-1); I should have typed 1/(e^(x-1)).

Answer 5

Well, @mathmale the parentheses don't make a difference in this case, but yes, in general @doryidina2 keep track of your delimiters.