Hey!
How do you do this problem by L'hospital.
$\displaystyle \lim_{x \to \infty} e^x-x^2 $
I know you can look at it and say $\displaystyle e^x$ is growing faster than $\displaystyle x^2 $.
Maclaurin Series -- from Wolfram MathWorld The one for e^x is there somewhere.
I don't care what the book wants, using l'Hopital's rule here is ridiculous.
By the time you figure out how to apply l'Hopital's rule to this problem, you could have solved it three other ways and gone on to answer a dozen other problems.
While I'm warmed up, I'll also say that l'Hopital's rule is the refuge of the lazy and the incompetent nine times out of ten.
I'm still a bit confused.
"using more than first 3 terms" is kinda vague. It still doesn't tell me how many terms I should use and why.
Also if we were to change the 2nd term in the original problem to something that is very similar e^x then would the substituting with the series work?