Nobody downloaded yet

Calculus for Business Economics - Math Problem Example

Comments (0) Cite this document
Summary
18. The volume of cylindrical can. The base surface area, and curved surface area. So according to the question. From this we can calculate h and put in the expression for the volume reducing the latter to a function of radius only.
28. Let us measure angle from the position of minute hand at 3 pm…
Download full paperFile format: .doc, available for editing
GRAB THE BEST PAPER98.4% of users find it useful
Calculus for Business Economics
Read TextPreview

Extract of sample "Calculus for Business Economics"

Download file to see previous pages Thus . Or .
12. Same procedure as in the question no. 10.
20.
(a) Given. So . Thus multiplying the two derivatives we get.
(b) Similar as part (a).
24.
(a) Given. Differentiating on both sides with respect to x, we get, which implies. So at given point (1, 2), the slope of the tangent to the curve is given by.

(b) Given. Differentiating on both sides with respect to x, we get, which implies. So at given point (0, 3), the slope of tangent to the curve is given by.
50. Take the road towards east as x-axis and that towards north as y-axis. So their intersection is the origin.

Set the clock at 0 at noon. After t hours the truck will be at point A (0, 70t) and the car will be at B (105(t-1), 0). So the distance S = AB is given by, which is equal to or simply. Thus . So required rate of change of distance at t = 2 is.
52. The quantity produced by the worker is given by.
(a) So R(t) = Q'(t) =
(b) Setting clock at 0 at 8:00 am., the time at 9:00 am is represented by t = 1. So R(1) =.
(c) The time 9:06 am is represented by t = 1.1. So Q(1.1) - Q(1)R(1).(1.1 - 1) = (27)(0.1) = 2.7.
(d) Q(1.1) - Q(1) = Q(1.1)- 27 can be calculated by actually substituting t = 1.1 in the expression for Q(t).
56. Given no. of units manufactured by the relation. The cost is given by. Now . So at t = 2, it is equal to 1663.2.
58. Letbe the error in the measurement of radius r. And be the error in the measurement of surface area. Here. So . That is, % error in S = 2(% error in r). As % error in S is no greater than 8%. So the largest % error in r is 4%.
Chapter 3
18. Given. For critical values we solve or. This gives. Also, which is +ve for and is -ve for . So at there is a relative minimum and at there is a relative maximum.
22. Given. So . This gives the critical...
Equating 6t and 90 + 0.5t, we can get t.
Set the clock at 0 at noon. After t hours the truck will be at point A (0, 70t) and the car will be at B (105(t-1), 0). So the distance S = AB is given by, which is equal to or simply. Thus . So required rate of change of distance at t = 2 is.
58. Letbe the error in the measurement of radius r. And be the error in the measurement of surface area. Here. So . That is, % error in S = 2(% error in r). As % error in S is no greater than 8%. So the largest % error in r is 4%.
(a) The fence is on all the four sides of the pasture. So 2(x + y)= 320. Thus y = 160 - x. Therefore the area A = xy = x(160 - x) =. . On equating it with 0, we get x = 80. So y = 80. These dimensions give maximum area.
28. The traffic speed is given by. Where t represents the time in hours measured 0 at noon. So . The critical values are given by. Or . Thus t = 1 and t = 5. Also . It is -ve for t = 1 and is +ve for t = 5. Therefore, the traffic speed is fastest at 1 hour past noon that is at 1:00 pm. It is slowest at 5 hours past noon that is at 5:00 pm.
30. Let the breadth = x in. So the length = 2x in. If height = y in, then the . Thus . Now the area of the four walls and the bottom equals. The area of the top is. Therefore cost of the material used is. Its derivative can be equated with zero to get the value of x.
40. Let the coffee break occurs after x hours. ...Download file to see next pagesRead More
Cite this document
  • APA
  • MLA
  • CHICAGO
(“Calculus for Business Economics Math Problem Example | Topics and Well Written Essays - 1000 words”, n.d.)
Retrieved from https://studentshare.org/business/1503304-calculus-for-business-economics
(Calculus for Business Economics Math Problem Example | Topics and Well Written Essays - 1000 Words)
https://studentshare.org/business/1503304-calculus-for-business-economics.
“Calculus for Business Economics Math Problem Example | Topics and Well Written Essays - 1000 Words”, n.d. https://studentshare.org/business/1503304-calculus-for-business-economics.
  • Cited: 0 times
Comments (0)
Click to create a comment or rate a document

CHECK THESE SAMPLES OF Calculus for Business Economics

Business Economics

...?Business Economics Q1 Discuss the reasons for the problems encountered in the market for housing over recent years. Analyze and evaluate the measures taken by both the industry and the government of a country of your choice to counter these problems, using specific examples to illustrate your arguments wherever possible. Introduction The very recent outburst of the housing price bubble in the most advanced and developed economies of the world has raised in serious concerns about the management of the macroeconomic tools, measures to combat the inflationary pressures especially by the public authorities, as that led to a financial crisis, and the consequences of the financial crisis had to be faced by the...
12 Pages(3000 words)Essay

Calculus

...The Calculus In its existence and approach, Calculus attempts to explore the grounds for the undefined nature of a function and designates a sensible understanding about up to which extent it would exist considering assumptions or applicable conditions. As in the rest of the significant fields in Mathematics, Calculus intellectuals had professed to work with a base knowledge of other math areas such as algebra and trigonometry to lay foundations and build on definitions, postulates, and theorems in conveying the purpose of the course and attain to its end thereafter. During elementary level of math education, one merely learns that divisibility by zero is not in any way valid or possible...
2 Pages(500 words)Essay

Business Economics

...? Business Economics Percentage Unemployment Rate (UK, the EU & the USA) Source: Office of National Statistics (2013) Unemployment is termed as the lack of occupation that leads to self sustainability in an economic perspective. According to Koos and Granata 2008, unemployment is one of the world’s most difficult agenda as it seeks to deter economic growth of a specific country or state and the entire world. Of importance to note is that, countries with a high level of unemployment have the worst economic growth while those that have a low rate of unemployment experience better economic growth (Lange 1998). As such, it is argued that, unemployment is directly related to economic growth of any given state or country. Consequently... that,...
6 Pages(1500 words)Essay

Calculus project

...Vectors and the Geometry of Space Q1. A scalar quantity is fully described or specified using its magnitude or value. For example one has to specify mass of a ball; then saying 2 kg would suffice. Similarly, distance traveled by a person in his morning walk will be a few kilometers. It is not at all required whether he went towards North – East and then took a left turn and then right turn at 60o and so; not none of this is required. In fact no directional information or any reference to any co-ordinate system is required while specifying a scalar quantity. Therefore, it is only natural that value of a scalar quantity is independent of the choice of the coordinate system. Q2. A scalar quantity can be either negative or zero... and the...
4 Pages(1000 words)Lab Report

Pre-Calculus

...Pre-Calculus Opposite (5) hypotenuse 89) Adjacent (8) X = Arctan =(opposite/adjacent) = 5/8, but cotx = 1/tanx So cot(actan) =8/5 X = arcsin (opposite/hypotenuse) =(-√2/2), but secx = 1/sinx, hence sec(arcsin -√2/2) = -2/√2 2. The value of the following without using calculator, a. tan-1(-√3/3). Let x = tan-1(-√3/3) = tan-1(-√3/3)x√3, hence tanx =-1/√3-3, tan2x=1/3√3, but 1+tan2x=sec2x, thus sec2x=1+1/3 =4/3, secx=1/cosx=2/(√3-3√3), but cos√3+ or -√3-3/2, which can be written as cosx = (√3-3)/2√3, hence x=π/6. From the quadrant, cosine is negative only on 2nd and 3rd , so the solution for will be in quadrants where tan is negative 2rd and 4th, so solutions are 11 π/6 and 5 π/6. b. cos-1(1), from the quadrant the...
1 Pages(250 words)Speech or Presentation

Business Economics

...Business Economics i Solution to Question One Unlike prices of other fuels, the prices of gasoline keep fluctuating. This is normally due to the changes in supply of crude oil. World events and domestic issues in oil-producing countries are normally the major causes of disruption in the supply of crude oil. Seasonality is also another cause of the fluctuation. In seasons like summer, when people tend to drive more, the prices of gasoline tend to rise due to the high demand (Stone, 2008). In winter, it is vice versa. Product supply and demand imbalances also cause the prices of gasoline to fluctuate. This is so because at times demand rises unexpectedly or supply declines suddenly due to production...
3 Pages(750 words)Speech or Presentation

Pre Calculus

...Pre Calculus Part 1. The Product Rule Solutions The derivative of f(x) = g(x) h(x) is given by f (x) = g(x)h (x) + h(x) g (x) (Larson, 2012). a. f(X) = (7X + X-1)*(3X + X2) Let g(x) = (7X + X-1) and h(X) = (3X + X2) Therefore, f (X) = (7X + X-1) (3 + 2X) + (3X + X2) (7 -X-2) = 21x + 14x2 + 3x-1 + 2 + 21x – 3x -2 + 7x2 – 1 f (X) = 42x + 21x2 +3x-1 -3x -2 +1 b. . f(X) = (X0.5)*(5-X) Let g(x) = (X0.5) and h(x) = (5-x) f (x) = (x1/2) (1) + (5-x) (1/2x -1/2) f (x) = x1/2 + 2.5x -1/2 – x3/2 c. f(X) = (X3 + X4)*(50 + X2) Let g(x) = (X3 + X4) and h(x) = (50+x2) Therefore, f (X) = (X3 + X4) (2x) + (50 + x2) (3x2 + 4x3) = 2x4 + 2x5 + 150x2 + 200x3 + 3x4 +4x5 f (X) = 5 x4 + 6 x5 + 150x2 + 200x3 2. Use the Chain Rule to find...
2 Pages(500 words)Assignment

Uses of calculus in business

...of all the 250 houses. On the other hand, differentiation has also been used to perform various business activities in the contemporary society for example it has been widely used to calculate the maximum sizes of packaging materials with a few known dimensions while missing other important dimensions. A real example of the application of differentiation has been evident i.e. in a scenario where a sales person wants to determine the maximum size of a packaging box with a known length= x and known width= y, but without a known height. This can be arrived at as: Volume= length. Width. Height also expressed as; V= l.w.h also; V (h)= (l-h). (w-h). h Bibliography Thompson, H. E.2011. Applications of...
2 Pages(500 words)Research Paper

Calculus Concepts

...Calculus ID Calculus Functions can be expressed as implicit or explicit based on the arrangement of the dependent and independent variables. For a function to be termed as explicit, it is usually given in terms of the independent variables. For instance, say a function y = f(x). It can be seen explicitly that y is the dependent variable and x variable is the independent variable. This means that y is the subject of the formula. The value of y is dependent on the values of x. On the other hand, implicit functions are usually expressed as the dependent and independent variable. For instance, a function y +3x +2 = 0 is expressed with both dependent and independent variables. Although implicit functions can...
3 Pages(750 words)Assignment

Calculus

...Introduction The birth of Calculus, in the 17th Century, is attributed to Sir Isaac Newton and Gottfried Wilheim von Leibniz. Even though they are the primary founding fathers of Calculus, they developed it independently and perceived the fundamental concepts in contrasting manners. For instance, Newton perceived the applications of Calculus as being geometrical and having a strong link to the physical world. He even used Calculus to try to explain how planets orbit around the sun. On the other hand, according to Leibniz, Calculus entailed analyzing the changes in graphs (Simmons 67). Newton-Leibnitz Controversy Their professional backgrounds played a...
2 Pages(500 words)Coursework
sponsored ads
We use cookies to create the best experience for you. Keep on browsing if you are OK with that, or find out how to manage cookies.

Let us find you another Math Problem on topic Calculus for Business Economics for FREE!

Contact Us