Preview

International Business

Satisfactory Essays
Open Document
Open Document
2080 Words
Grammar
Grammar
Plagiarism
Plagiarism
Writing
Writing
Score
Score
International Business
University of Business Technology

UBT – CEIT
CALCULUS I – MATH 101
FALL – 2012
Instructor : Abdulraheem Zabadi
STUDY GUIDE

Table of Contents
Limits
Differential Calculus
Integral Calculus
SOME USEFUL FORMULAS Chapter One : Limits

Properties of Limits
If b and c are real numbers, n is a positive integer, and the functions ƒ and g have limits as x → c , then the following properties are true.

Scalar Multiple : limx→c (b f(x))=b limx→c fx

Sum or difference : limx→c ( fx± g(x)) = limx→c fx ± limx→c ( gx)

Product : limx→c (fx. g(x)) = limx→c fx . limx→c gx

Quotient: limx→c fxgx = limx→cf(x)limx→cg(x) , gx≠0

One-Sided Limits limx → a+fx x approaches c from the right limx → a-fx x approaches c from the left

Limits at Infinity limx →∞f(x) = L or limx → -∞f(x) = L The value of ƒ(x) approaches L as x increases/decreases without bound. y = L is the horizontal asymptote of the graph of ƒ.

Some Nonexistent Limits limx→01x2 limx→0 xx limx→0sin1x Some Infinite Limits

limx→01x2= ∞ limx→ 0+ ln x= - ∞

Exercise: What limx→0sinxx ?

a. 1 b. 0 c. ∞ d. DNE
The answer is a ( you should memorize this limit)
Continuity
Definition : A function ƒ is continuous at c if:
1. ƒ(c) is defined 2. limx→cfxexists 3. limx→cfx= fc

Graphically, the function is continuous at c if a pencil can be moved along the graph of ƒ(x) through (c, ƒ(c)) without lifting it off the graph.

Exercise: If f(x) = 3 x2+x2x , for x x ≠0 f(0) = k and f is continuous at x = 0 , find the value of k ? a. -32 b. 32 c. -1 d. 0 e.1 , answer is b

Intermediate Value

You May Also Find These Documents Helpful

  • Good Essays

    Compositions and Inverses

    • 696 Words
    • 3 Pages

    Next we are to compose two pairs of the functions into each other. First we…

    • 696 Words
    • 3 Pages
    Good Essays
  • Satisfactory Essays

    Composition and Inverse

    • 486 Words
    • 2 Pages

    Next we are to compare two pairs of the functions into each other. First we will work out.…

    • 486 Words
    • 2 Pages
    Satisfactory Essays
  • Good Essays

    International Business

    • 748 Words
    • 3 Pages

    Q: List elements of the national business environment that influence the standardization-versus-adaptation decision. Standardized is just one of a number of strategies with which firms successfully enter the international marketplace today. Standardization may not always be the most appropriate strategy, even. Smaller companies may also be better off adapting to local cultures and exploiting their international image to gain market share locally. Consumers in different national markets often demand products that reflect their unique tastes and preferences. Cultural, political, legal, and economic environments have a great deal to do with the preferences of both consumers and industrial buyers worldwide. A culture’s aesthetics involves, among other things preferences for certain colors.…

    • 748 Words
    • 3 Pages
    Good Essays
  • Satisfactory Essays

    International Business

    • 6596 Words
    • 27 Pages

    1) ________ consists of specific learned norms based on attitudes, values, and beliefs of a group of people.…

    • 6596 Words
    • 27 Pages
    Satisfactory Essays
  • Good Essays

    Math 135 Final Exam Paper

    • 1922 Words
    • 8 Pages

    Math 135 Final Exam Study Guide The graph of a function is given. Follow the directive(s). 1)…

    • 1922 Words
    • 8 Pages
    Good Essays
  • Powerful Essays

    International Business

    • 1964 Words
    • 8 Pages

    The Freedom in the World survey provides an annual evaluation of the state of global freedom as experienced by individuals. The survey measures freedom-the opportunity to act spontaneously in a variety of fields outside the control of the government and other centers of…

    • 1964 Words
    • 8 Pages
    Powerful Essays
  • Powerful Essays

    C2 Paper

    • 827 Words
    • 4 Pages

    Candidates may use any calculator EXCEPT those with the facility for symbolic algebra, differentiation and/or integration. Thus candidates may NOT use calculators such as the Texas Instruments TI 89, TI 92, Casio CFX 9970G, Hewlett Packard HP 48G.…

    • 827 Words
    • 4 Pages
    Powerful Essays
  • Satisfactory Essays

    4. Let f (x) = xx−1 on [0, 2]. Show that there is no value of c such that f (c) =…

    • 320 Words
    • 2 Pages
    Satisfactory Essays
  • Satisfactory Essays

    Questions on Mathematics

    • 1037 Words
    • 21 Pages

    The equation f(x) : 0 has another root B in the interval [-1, 0]. Starting with this…

    • 1037 Words
    • 21 Pages
    Satisfactory Essays
  • Good Essays

    International business

    • 745 Words
    • 3 Pages

    Semicontronics is an Australian manufacturing company that has been in the business of semi manufactured electronics for over a decade. Semicontronics has a solid reputation for meeting customer demands for quality products on time and on budget. The majority of Semicontronics customers are international, mid-market manufacturing companies that produce generic electronics such as cell phones, digital media players and game consoles. Retail stores in foreign countries purchase the generic products and rebrand them for sale.…

    • 745 Words
    • 3 Pages
    Good Essays
  • Satisfactory Essays

    International Business

    • 409 Words
    • 2 Pages

    In what kind of industries does a localization strategy make sense? When does a global standardization strategy make most sense? The industry that localization strategy would make sense would be the automotive industry, manufacturing factories, and I want to stay the big chain grocery stores. By these firms customizing the products they offer to local demand, the firm increases the value of that product in the local market. But on the downside, it involves some duplication of functions. The strategy may make sense, however, if the added value associated with local customization supports higher pricing, which enables the firm to recoup its higher costs, or if it leads to substantially greater local demand, enabling the firm to reduce costs through the attainment of some scale economies in the local market. When global standardization strategy make most sense is when the firm try not to customize their product offering and marketing strategy to local conditions because customization involves shorter production runs and the duplication of functions, which tends to raise costs. Instead, they should prefer to market a standardized product worldwide so that they can reap the maximum benefits from economies of scale and learning effects.…

    • 409 Words
    • 2 Pages
    Satisfactory Essays
  • Good Essays

    | logb(−4), for example, makes no sense. Since b is always positive, no power of b can produce a negative number.…

    • 3127 Words
    • 13 Pages
    Good Essays
  • Good Essays

    On the same Cartesian Coordinate plane, sketch the graphs of each set of exponential function…

    • 904 Words
    • 4 Pages
    Good Essays
  • Satisfactory Essays

    Note: When a line meets a curve there will be 0, 1, or two solutions.…

    • 262 Words
    • 2 Pages
    Satisfactory Essays
  • Good Essays

    Math oral studyguide

    • 3110 Words
    • 13 Pages

    When we can trace the function without lifting the pencil. Continuity requires general limit existing, function is defined at x, and they are equal to each other. Jump disc. Point disc., vertical asymptotes,…

    • 3110 Words
    • 13 Pages
    Good Essays

Related Topics