SOLUTION: evaluate the limit! Lim (e^4t) -1/t x->0 i thought e^0=1 t=0 so 0/0 =0 but it said it was wrong i also tried infinity but it was wrong

Question 592472: evaluate the limit!
Lim (e^4t) -1/t
x->0
i thought e^0=1 t=0
so 0/0 =0 but it said it was wrong
i also tried infinity but it was wrong
Answer by ntnk(54) (Show Source): You can put this solution on YOUR website!
I think your parentheses are misplaced, so based on the work you have shown, my guess is that your question is the following:
http://latex.codecogs.com/gif.latex?%5Clim_%7Bt%5Cto%200%7D%5Cfrac%7Be%5E%7B4t%7D-1%7D%7Bt%7D
First I would like to point out and emphasize the fact that 0 / 0 is not the same as 0. (However, you are correct that .)
The easiest way to solve this is by using L'Hopital's rule. We can take the derivative of the numerator and the derivative of the denominator. The limit above is therefore given by the following
http://latex.codecogs.com/gif.latex?%5Clim_%7Bt%5Cto%200%7D%5Cfrac%7B4e%5E%7B4t%7D%7D%7B1%7D
Now we can plug in to find out that the limit is 4.
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