The power generated by a battery is given by the expression $P(t) = 25te^{-t^{2}/4}$, where $t > 0$ is the operating time.\ a) (0.5 points) Calculate the value towards which the power generated by the battery tends if left operating indefinitely.\ b) (0.75 points) Determine the maximum power generated by the battery and the instant at which it is reached.\ c) (1.25 points) The total energy generated by the battery up to instant $t$, $E(t)$, is related to power by $E'(t) = P(t)$, with $E(0) = 0$. Calculate the energy produced by the battery between instant $t = 0$ and instant $t = 2$.
The power generated by a battery is given by the expression $P(t) = 25te^{-t^{2}/4}$, where $t > 0$ is the operating time.\
a) (0.5 points) Calculate the value towards which the power generated by the battery tends if left operating indefinitely.\
b) (0.75 points) Determine the maximum power generated by the battery and the instant at which it is reached.\
c) (1.25 points) The total energy generated by the battery up to instant $t$, $E(t)$, is related to power by $E'(t) = P(t)$, with $E(0) = 0$. Calculate the energy produced by the battery between instant $t = 0$ and instant $t = 2$.