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# Elementary Calculus: Integers, Derivatives, 14 Questions

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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

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https://brainmass.com/math/calculus-and-analysis/elementary-calculus-integers-derivatives-questions-522110

#### Solution Preview

Please see the attached file. Hope it helps.

Introduction
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Rationale behind the Decision
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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.

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