Calculus Answers

Determine the following integral

∫  (1+cos^2 x  / 1+cos 2x ) dx

a.    1 / 2 [ tan x + x] + c

b.   1 / 2[1− 1 / cos x ] + c

c.    1 / 2 + c

d.   1 / 2 tan x + x + c

The demand function Q and cost function C(Q) of a commodity are given by the equations 

Q=20−0,01P,

C(Q)=60+6Q,

where P and Q are the price and quantity, respectively.

The total revenue function (TR) in terms of P is

a. TR=20−0,01P.

b. TR=P(120−0,01P^2).

c. TR=20P−0,01P^2.

d. TR=P2(20−0,01P^2).

A firm has the following total and cost functions:

TR=20Q−4Q^2

TC=16−Q^2,

where Q is the number of unites produced and sold (in thousands). How many units should be produced to maximise the profit?

a.3,3333,333 units.

b.1,7141,714 units.

c.1,3331,333 units.

d.3 3333 333 units.

The demand function Q(P) and cost functions C(Q) of a company's are given by the equations:

Q=12000−60P

(Q)=10000+4Q,

where P and Q are the price and quantity, respectively.

What is the company's profit function?

a.Profit=−60P−4Q+2 000

b.Profit=−60P^2+11 760P−58 000

c.Profit=−60P^2+12 240P−58 000

d.Profit=−60P^2+12 240P+38 000

The demand function Q(P) and cost functions C(Q) of a commodity are given by the equations:

Q=12000−60P

C(Q)=10000+4Q,

where P and Q are the price and quantity, respectively. 

The total revenue function TR in terms of P is

a. TR=12 000−60P.

b. TR=P(12 000−60P^2).

c.  TR=12 000P−60P^2.

d.  TR=12 000+60P^2.

Y =  1 /3  x^3  –  x^2 – 3x  +  2

Is

a. (−1, 11 / 3) is a maximum and (3,-7) is a minimum

b. (−1,0) is a maximum and (3,0) is a minimum

c. (3,0) is a maximum and (-1,0) is a minimum

d. (3,−7) is a maximum and (−1,11 / 3) is a minimum

F (x) = e^x  / x

is

a.      F’ (x) = e^x (x – 1) + e^x (x^2) – e^x (x -1) (2x) / x^4

b.      F’ (x) = e^x (x -1) / x^2 – e^x (x -1) (2x) + e^x (x^4)

c.      F’ (x) = e^x (x – 1) + e^x (x^2) – e^x (x -1) (2x) / x^2

d.      F’ (x) = e^x (x^2 – 2x + 2)   / x^3

F (x) = e^ (x^2 – 3x)

Is

a.      e ^ x^2 - 3x   /   2x – 3

b.      2x  e^ x^ 2 – 3x   +   3e^x^2 – 3x

c.      (2x – 3) e^x^2 -3x

d.      e^x^2   - 3^x