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- anonymous

Need help to understand this ( I apparently am not understanding something as I keep getting it wrong)
Find the limit. Use l'Hospital's Rule if appropriate. Use INF to represent positive infinity, NINF for negative infinity, and D for the limit does not exist.
Lim t-->0 (8 e^t -8)/t^3
Step 1: verify if indetermine form: because my denominator gives me 0, I consider it an indeterminate form
Step 2: I take the first derivative giving me
(8 e^t )/3t^2
still gives me 0 in the denominator so I go to the second derivative
Step 3: (8 e^t )/6t

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- anonymous

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- anonymous

I get 0 again so I do the third derivative giving me (8 e^t )/6 and I plug in 0 in t giving me 8/6. no? but the answer is infinity

- anonymous

But you got an 8 in the numeration 8/0 is not an indeterminate form

- anonymous

so wait, you're telling me when I use l'hospital rule , i need a 0/0 to apply it ? or is that example just an exception ? and I thought anything over 0 would give me an error, therefore being an inderminate form

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- anonymous

not necessarily 0/0 there is other forms such as \[\infty^0\] \[\frac{\infty}{\infty}\] etc.. your book should show all of them... however \[\frac{8}{0}\] is not one of them

- anonymous

my teacher didn't assign any books, so I work with internet , etc... I work with what i find :/ but thanks, so any number ( except 0 ) /0 is not inderminate. have a good night!

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