Explore BrainMass

Elementary Calculus: Integers, Derivatives, 14 Questions

1. Let f:Z->Z , where Z is the set of integers and f(x)=x^5+101
Is f(x) a one-to-one function?

2. Prove that f(x)=4x-3 is one-to-one function

3. The ceiling function maps every real number to the smallest integer greater than
or equal to that number, f:x->[x], where [x] is the smallest integer greater
than or equal to x. Is this function one-to-one? List five numbers that have
the same image

4. Find lim n^3 + n when n-> ?
n^2 - 1

5. Find lim 3x^7 + x^3 +17 , as x-> ?
2x^7 + X^2 + 1

6. Find lim x^2008 + 1 , as x-> ?
x^2009 + 1

7. Find lim x^4 + 111,111 , as x-> 0
x^3 + 111,111,111

8. Prove that f(x)=x^2-4 is a continuous function

9. Find derivatives of the following functions using differentiation rules

1. f(x)= 9x+5
2. f(x)= 3e^x
3. f(x)= 3x^3 + 4
4. f(x)= x^4 + 3x^2 + 4x - 31
5. f(x)= (2x + 3)e^x
6. f(x)= (2x-1)e^(x-3)
7. f(x)= x(x-2)^2 =x(x^2 - 4x + 4) = x^3 - 4x^2 + 4x

10. Find the derivative of the following function at x0 = -1

f(x)=3x^2 + x + 1

11. Find differentials of the following functions:
1. f(x)= 3x^2 + x + 1
2. f(x)= e^(x-1)
3. f(x)= -e^x + x^3 - 4

12. Let f(x)= x and g(x)=x^2 , where xER
Find f?g and g?f as well as the domain and range of these functions.
13. Prove using the definition that lim 1/n^2 = 0 , when n-> ?
14. Find the derivative of f(x)=1/x by using the definition of the derivative

Please see the attached document for full details.


Solution Preview

Please see the attached file. Hope it helps.

In the organization, strategies play an important role in order to formulate the business and to expand the business at international platform. Effective and proper strategies also help the companies to increase in the customer base and to provide an opportunity that support the companies to improve their business in the national and international market place. Implementation of proper strategies for the companies also helps the organizations to achieve competitive advantages over competitors in significant way (Dalic, 2007). In this guideline discusses the plan and the important items that will need to cover. This guideline also covers the importance of globalization for the company and the positive and negative aspects of the decision of globalization.
In addition, this guideline also discusses the suitable geographic location for the company for global expansion. This guideline also explores the importance of decision in order to support the goals of growth and expansion of the company. At the end, this guideline also provides the arguments for the opposite perspective of the decision.
Globalization for the Company
Globalization refers to the expansion of business in the global market. In the other words, globalization is an approach that links the business activity to the international market. With the help of globalization, an organization can also achieve the competitive advantages over the competitor in the national and international market. Through the globalization approach, companies also receive the international frame for the business that supports in increases in customers base as well as their profits. The globalization approach is also helpful for the companies in order to make effective strategies for the customers and to increase the business in national and international market. Globalization helps the companies to make a better platform for the business strategies and implement these strategies in order to generate business and achieve targeted profits from the various markets (Frost, 2003).
For the custom furniture manufacturer company, it is a good move to go global. Through the implementation of globalization approach in the company, organization can effectively implement its strategies and marketing plan in order to achieve competitive advantages. Due to the global world, furniture manufacturing business has effective demand in the international market and many furniture companies create export and import of furniture that are made in the different countries. The move for globalization helps the company to increase the demand of furniture that can support the company to improve in customer base (Bettignies & Lepineux, 2009). The globalization moves always a god move for the furniture company in order to take advantages from the international market.
Through the globalization, company is able to link efficiency and productivity with the needs and demands of the international customer. This helps the company to provide quality products to the customers with the low cost. It is also identified that with the move of globalization most of the manufacturing companies are able to increase in demand of the products. It is because going international helps the company to develop the healthy relationship with the customers that supports the company to improve the demand of the products and services in the international market (Daft & Marcic, 2010).
Rationale behind the Decision
The rationale behind taking this decision is related to the development of activities in the national and international market. With the help of globalization, Furniture Company can improve actions and activities to serve and cover most geographic area for the furniture products. Through the globalization, company can also generate more profits and improve the financial condition in the market. Through the implementation of globalization approach in the company, organization can also provide furniture products to the international customers. Through the globalization approach, organization can also effectively use its available resources that can support the company to satisfy the current or existing customers (Korine & Gomez, 2002). This can also lead the company to attract new customers in the national and international market.
The move of globalization is also helpful for the company to maintenance the relationship with the customers. It is identified that globalization approach help companies to make effective relationship with the customers through providing services and products on time. The implementation of globalization approach and activities in the organization, company can also improve its transportation system that can help the company to provide better services to the right customers on time (Heslam, 2004). This can support company to improve its relationship with the international customers more effectively.
The rationale behind to take this decision is also related to the implementation of global strategies to achieve competitive advantages from the international market. Through the decision of globalization, company can be able to formulate the global marketing and business strategies that can support company to provide a global recognition for the company. Globalization can also help the company to improve its efficiency in the market. It is because through the global expansion, company needs to recruit international managers in order to effectively ...

Solution Summary

Elementary calculus for integers and derivatives are examined.