Question

Pumping stations deliver oil at the rate modeled by the function D, D(t)=5t/1+3t with t measure in hours and and D(t) measured in gallons per hour. How much oil will the pumping stations deliver during the 4-hour period from t = 0 to t = 4? Give 3 decimal places.

Answer 1

@iambatman @ganeshie8

Answer 2

@nikato

Answer 3

@dan815

Answer 4

any interval is t2 - t1

so find D(4) - D(0)

Answer 5

1.538?

Answer 6

20/13-0=1.538

Answer 7

well 0/0 is not 0, have you learned derivatives?

Answer 8

yes, what would it be then aren't we just subtracting?

Answer 9

correct, however 0/0 is indeterminate so you have to find another form of the equation.
use l'hopital's rule

take the derivative of the top and bottom and plug in x. do this until the answer isn't 0/0

Answer 10

can you please show me the steps on doing that?

Answer 11

sure let me type it up

Answer 12

thank you!!!

Answer 13

omg i'm so sorry this is all wrong, you were right, just subtract 0

Answer 14

its okay! & thanks :)

Answer 15

do you mind helping me with 3 more?

Answer 16

wow nope, still wrong let me type this back up, read it wrong really sorry

Answer 17

its okay :)

Answer 18

D(t) is the rate at which the oil is pumped and you want the amount, that's just going to be
\[\int\limits_{0}^{4}f(x)dx\]sorry about all that

Answer 19

and this time i'm positive this is the answer

Answer 20

got it :) thanks

Answer 21

would 0 be the answer?

Answer 22

http://www.wolframalpha.com/input/?i=derivative+of+integral&f1=f(x)&f=DerivativeIntegral.integrand_f(x)&f2=x&f=DerivativeIntegral.derivativevariable%5Cu005fx&f3=x&f=DerivativeIntegral.integralvariable_x&f4=0&f=DerivativeIntegral.rangestart_0&f5=4&f=DerivativeIntegral.rangeend%5Cu005f4

Answer 23

wait sorry

Answer 24

http://www.wolframalpha.com/input/?i=+integral&a=*C.integral-_*Calculator.dflt-&f2=f(x)&f=Integral.integrand%5Cu005ff(x)&f3=&f=Integral.variable_&f4=0&f=Integral.rangestart%5Cu005f0&f5=4&f=Integral.rangeend%5Cu005f4 i didn't get one

Answer 25

to do this by hand i'm pretty sure you need to do partial fractions, which i don't remember at all, but if you want to trust wolfram, it's not a total loss

Answer 26

kk :) thanks