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Quantitavi Methods

In: Business and Management

Submitted By alyoshak
Words 337
Pages 2
1. Prove that fx=2x+5 is one-to-one function.

2. Let f: A→B, as given below. Is f a one-to-one function? Please explain why or why not.

B
A

f

5
5
1

3
1

6
2

2
4
6

7
4

8
3

3. The modulo function (a mod n or a modulo n) maps every positive integer number to the remainder of the division of a/n. For example, the expression 22 mod 5 would evaluate to 2 since 22 divided by 5 is 4 with a remainder of 2. The expression 10 mod 5 would resolve to 0 since 10 is divisible by 5 and there is not a remainder. a. If n is fixed as 5, is this function one-to-one?

b. List five numbers that have the exact same image.

4. Find limn→∞n2-1n3+n

5. Find limx→∞x1001-xx1000+x

6. Find limx→∞8x6+4x4-3x2x6+x5-7

7. Find lim2x99+x+1,000,000x100+2,000,000 as x→0

8. Prove that fx=x2+7 is a continuous function.

9. Find derivatives of the following functions using differentiation rules. (Do not use the definition of a derivative!)

c. fx=2x+5

d. fx=2x5+x3-6x+100

e. fx=ex+2(4x-1)

f. fx=7ex

g. fx=x2(x-1)

h. fx=3x2+7

i. fx=ex(2x+5)

j. fx=ex+2+4x-1

10. Find the derivative of the following function at : fx=2x3+x2+9

11. Find the derivative of the following function fx=2x2-x using the definition of a derivative. (Hint: though you can use the rules of differentiation to check your answer, you must use the definition of a derivative to solve this problem in order to receive any credit for your response)

12. Let fx=2x and gx=ex, where. Find and as well as the domain and range of these functions.

13. Find the derivative of by using the definition of the

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