Homework 4.2

1.  A coffee company has found that the marginal​ cost, in dollars per​ pound, of the coffee it roasts is represented by the function​ below, where x is the number of pounds of coffee roasted. Find the total cost of roasting 180 lb of​ coffee, disregarding any fixed costs.

$C‘\left(x\right)=–0.018x + 6.75, for x\le 300$

The total cost is ____

2  A note card company has found that the marginal cost per card of producing x note cards is given by the function​ below, where

is the marginal​ cost, in​ cents, per card. Find the total cost of producing 540 ​cards, disregarding any fixed costs.

$C‘\left(x\right)= 0.08x+76, for x\le 1000$

The total cost is ____

3.  A juice company has found that the marginal cost of producing x pints of​ fresh-squeezed orange juice is given by the function​ below, where

is in dollars. Approximate the total cost of producing 279 pt of​ juice, using 3 subintervals over

and the left endpoint of each subinterval.

$C‘\left(x\right) = 0.000003x^2–0.0015x+4, for x\le 350$

The total cost is about ______

4.  Write the series in summation notation. 7 + 14 + 21 + 28 + 35 + 42

5.  

   without using summation notation

6. Approximate the area under the graph of  

over the interval 

  using 5 subintervals. Use the left endpoints to find the height of the rectangles.

The area is approximately

7.  Use geometry to evaluate the definite integral.

${\int }_0^{4}8 dx$

8.  Use geometry to evaluate the definite integral.

${\int }_0^{5}x dx$