calculus

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A 12,000 liter tank filled to capacity at t=0 drains at rate r(t), measured in liters per hour, where r is defined as piece-wise function:
r(t)={ (600t)/(t+3), [0,5]
{1000e^(-0.2t), (5,infinity)

Is r continuous at t=5? Show work that lead to you answer.

• calculus -

at t=5,

600t/(t+3) = 3000/8 = 375
1000e^(-.2t) = 1000/e = 367.8

Actually, the computation isn't really necessary, since r(t) is rational at t=5, and e^x is irrational for any rational x.

• calculus -

• calculus -

it means that the two piecewise functions don't have the same value at t=5, so r(t) cannot be continuous.

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