Calculus homework

MA 141 6.1 Turn in Homework

Name _________________________

1. Find the following antiderivatives, (or indefinite integrals). Simplify!

a.) (#30) 2(2 2 )xx x e dx  

b.) (#36.) 3 2 2

1 x dx

x

   

  

c.) (#40) 2 2 4(1 )u u u du  

d.) (#44) ( ) 3

2 xx e dx x

    

  

e.) (#48) 3 3

2 ( ) t t

dt t

 

2. (#54). Find f(x) to that it satisfies: 1

'( )f x x

 ; and f(4) = 2.

3. (#58) Find f(x) to that it satisfies: 1

'( ) 1 xf x e x

   ; and (1) 3f e 

4. The velocity (in fee/second) of a maglev is v(t) = 0.2t + 3 (0 < t < 120). At t= 0, it is at the station. Find the function giving the position of the maglev at time t, assuming that the motion takes place along a straight stretch of

track.

5. (#68). The management of Lorimar Watch Company has determined that the daily marginal revenue

function associated with producing and selling their travel clocks is given by '( ) 0.009 12R x x   where x

denotes the number of units produced and sold and '( )R x is measured in dollars/unit.

a.) Determine the revenue function R(x) associated with producing and selling these clocks.

b.) What is the demand equation (p as a function of x) that relates the wholesale unit price with the

quantity of travel clocks demanded? (Remember: R = xp.)

6. (#70) Carlota Music Company estimates that the marginal cost of manufacturing its Professional Series guitars is '( ) 0.002 100C x x  dollars/month when the level of production is x guitars/month. The fixed costs incurred by

Carlota arte $4000/month. Find the total monthly cost incurred by Carlota in manufacturing x guitars/month.

7. Cannon Precision Instruments makes automatic electronic flashes with Thyrister circuitry. The estimated

marginal profit associated with producing and selling these electronic flashes is '( ) 0.004 20P x x  

dollars/unit/month when the production level is x units per month. Cannon’s fixed cost for producing and

selling these electronic flashes is $16,000/month.

a.) At what level of production does Cannon realize a maximum profit?

b.) What is the maximum monthly profit?