Calculus Answers

1. (a) if f(t)=e^-wt sin wt, show that d^2f/dt^2 +2w df/dt + 5wf=0

(b) A curve passes through the points (1, 2) and its gradient function is 3x^4-1 all over X^2. Find the equation of the curve.

Differentiate the following with regard to x : y=(cosec x +2tanx)^3

Question  14

The supply function of a good is given by

P_s = Q² − 2Q + 12.

Determine the producer surplus if ten units are supplied (Q = 10) at price P.

[1.     353,33

[2.     686,67

[3.     566,67

[4.     1273,33

Questions 11, 12  and  13  are  based  on  the  following  information: If a marginal revenue function of a rm is given as

MR = 10Q² + 6Q − 3,

 where Q is the number of units sold.

11

Find an expression for the total revenue function (TR).

1. ¹⁰/₃ Q³ + 3Q² - 3Q + C
2. ⁵/₃ Q³ + 6Q² - 3Q + C
3. Q³ + 3Q² - 3Q + C
4. ³/₅ Q³ + 3Q² - 3Q + C

12

Find the total revenue function if it is given that TR = 0 when Q = 0.

1. ¹⁰/₃ Q³ + 3Q² - 3Q
2. ⁵/₃ Q³ + 6Q² - 3Q + 1
3. Q³ + 3Q² - 3Q + 3
4. ³/₅ Q³ + 3Q² - 3Q

   13

Calculate the firm's total revenue when 5 units are sold.

[1      310,36

[2      200,00

[3      476,67

[4      532,67

Q 10

A tool hiring company has estimated that the rate of increase in the maintenance cost of power drills is given by the equation

C(t) = 2 + t^1,5,

where t is the time that the company is in operation for weeks. Calculate the total maintenance cost during the first four weeks.

1.      10

2.      22.36

3.      20.8

4.      32.36

Question  9

The marginal cost function for a good is given by

MC = −Q² + 80Q.

Find the total cost function if fixed costs are   500.

1. -^Q3/₃ +40 + 50
2. ^Q3/₃ +40Q² + C
3. -^Q3/₃ +80Q² + C
4. Q³ +80Q² + 500

8.Given the demand function P_d = 35 − Q²

and the supply function P_s = 3 + Q².

Calculate the producer surplus for the supply function.

1.      0,0

2.      33,3

3.      69,0

4.      42,7

Question  7

Calculate the consumer surplus for the demand function

P = 25/ Q + 2

when the market price P = 5.

1.      2,3

2.      15,0

3.      7,9

4.      25,2

Evaluate the definite intergral "\\int"₀¹ 18e^3x+1dx (round to an interger).

1.         322

2.         311

3.         932

4.             965

how many terms of the arithmetic series 10 + 8 + 6 +... will make the sum 24?