MarcLeclair 2 years ago 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

1. MarcLeclair

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

2. Outkast3r09

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

3. MarcLeclair

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

4. Outkast3r09

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

5. MarcLeclair

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!