(finite difference ¿¬½À¹®Á¦)

 


#1

     Generate a difference table for the linear function y = 3x - 5 for 1 ¾ x ¾ 8.

#2

       Generate a difference table for the general linear polynomial y = ax + b for 1 ¾ x ¾ 8.

#3

        Repeat problem #1 for the cubic polynomial y = 2x^3 - x^2 + 3x + 1 for 1 ¾ x ¾ 8.

#4

        Repeat problem #2 for the general cubic polynomial y = ax^3 + bx^2 + cx + d for 1 ¾ x ¾ 8.

#5

       Complete the difference table for the values in the function y = f(x) shown here.

 

x

1

2

3

4

5

6

f(x)

12

28

50

78

112

152

D1

D2

D3


    What type of function is this ?   How do you know?

#6

       Determine an explicit representation for the relationship defined in problem #5.

#7

       The table here shows values for x greater than 2. Use the method of constant differences to determine an explicit representation for the relationship shown and then use it to determine f(1) and f(2).

 

x

3

4

5

6

7

8

f(x)

64

141

266

451

708

1049

     

#8

       Determine an explicit representation for the relationship shown in the table below.

     

x

1

2

3

4

5

6

h(x)

4

23

86

247

584

1199

     

#9

       The pattern below is formed by rotating the standard multiplication table 45 degrees clockwise. Continue the pattern for at least two more rows. Then determine a generating function that can be used to calculate the sum of any row. Use it to determine the sum of the 100th row.

      

    1
    

    2     2
    

    3     4     3
    

    4     6     6     4
    

    5     8     9     8     5

 

     

#10

       Determine an explicit representation for the sum of any row in the infinite array whose first three lines are shown here.

  

    (1 x 2) =
    

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

    (1 x 2) + (2 x 3) + (3 x 4) =