Question

Calculate the following limit:

Answer 1

\[\lim_{t \rightarrow 0}\frac{t^4e^t + 10t^3e^t + 12t^2e^t - 24te^t+24e^t-24}{t^5}\]

I'm doing this myself but I want someone else to do it with me because I'll probably mess up somewhere

Answer 2

I'll do it xD

Answer 3

I wanted to try and factor a bit of the numerator but it won't work, I'm gonna need to do the long way. Here we go

Answer 4

I got 28/5

Answer 5

hold up..almost done

Answer 6

@mhchen my opinion this ton power of 5 when t going to zero is zero - yes ? so than you divide anything what you get in numerator so this not can being what you ve got ...

Answer 7

t on power of 5

Answer 8

like an idea - hope you understand me

Answer 9

I got infinity, and it makes sense with the greatest magnitude function at the bottom, as jhonny9 mentioned

Answer 10

yes sure bc. in numerator this term of e^t when t going to zero so this reszult 1 bc. ever number on power of zero is 1 so this mean that this term of e^t dont make nothing inside this equation

yes ?

Answer 11

in this case 24-24 is equal zero