Question

I have a couple of questions and i wanted to know if my answers are correct. Thanks in advanced!

1. Determine the values of x for which the function f(x)=x+2/x-2 is discontinuous

Would the answers be x=2 because the function would be undefined?

2. An oil tank is being drained for cleaning. After t minutes there are v litres of oil left in the tank, where v(t)=35(25-t), 0<=t<=25
a) determine what v(25) represents

I substituted t+25 into the equation and got 0 as my answer. Would the 0 represent that the tank is completely drained?

b) determine the average rate of change of volume during the first 15 minutes

i got -1225 as my answer (would there be a unit, like litres?)

c) determine the rate of change of volume at the time t=15 minutes

is the question asking for the instantaneous rate of change? i'm not sure what they are asking for

Answer 1

your value x=2 is correct.

a) yes, but v(25) represents the amount of fluid remaining after 25 minutes. It just happens also to be true that at that time the tank is empty.

b)
v(0) = 875
v(15) = 350
volume changed by -525 in 15 minutes, for an average rate of change of

-525L/15min = -35 L/min

c) the rate of change is constant: -35L/min since

v(t) = -35t + 875

instantaneous rate of change is the derivative

v'(t) = -35