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melomori [17]
3 years ago
10

---- PLEASE HELP <3 .. with steps :( <3

Mathematics
1 answer:
Zielflug [23.3K]3 years ago
5 0

1) 6, 18, 54

2) 5/3, 14/9, 41/27

3) 1.5, 2.5, 2.5

Step-by-step explanation:

1)

The function that we have in this problem is

g(x)=3x

We want to find the first 3 iterations.

The initial value is:

x = 2

To find the value of the 1st iteration, we just substitute this value into the expression of the function, and we get:

g_1(x)=3x=3\cdot 2 = 6

The to find the value of the 2nd iteration, we just substitute this value into the expression of the function, and we get:

g_2(x)=3\cdot g_1(x)=3\cdot 6 = 18

Finally, the 3rd iteraction is given by:

g_3(x)=3g_2(x)=3\cdot 18=54

2)

Here in this problem the function that we have to use is

g(x)=\frac{1}{3}x+1

The initial value is

x=2

So the first iteration is given by

g_1(x)=\frac{1}{3}\cdot 2 + 1 = \frac{5}{3}

To find the 2nd iteration, we substitute this value into g(x) again:

g_2(x)=\frac{1}{3}g_1+1=\frac{1}{3}\cdot \frac{5}{3}+1=\frac{5}{9}+1=\frac{14}{9}

Finally, to find the 3rd iteration, we substitute this value into g(x) again:

g_3(x)=\frac{1}{3}\cdot \frac{14}{9}+1=\frac{14}{27}+1=\frac{41}{27}

3)

The function in this problem is

g(x)=-|x-2|+3

The initial value is

x = 0.5

So, the first iteration is:

g_1(x)=-1|0.5-2|+3=-1|-1.5|+3=-1\cdot 1.5 +3=-1.5+3=1.5

The second iteration is given by

g_2(x)=-|g_1-2|+3=-|1.5-2|+3=--0.5+3=2.5

Finally, the 3rd iteration is

g_3(x)=-|g_2-2|+3=-|2.5-2|+3=-0.5+3=2.5

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