Question

What is the third iterate of the function f(x) = √50 – 3x if x0 = 5.7? Round to three decimal places as needed.A. x3= 5.721B. x3= 5.729C. x3= 5.726D. x3= 5.736

Answer 1

The function is given below as

`f(x)=√(50-3x),x_0=5.7`

Concept:

The iteration formula will be given below as

`x_(n+1)=√(50-3x_n)`

Step 1:

To figure out the first iteration, we will use the formula below

`\begin{gathered} x_1=f(x_0) \\ f(x_0)=√(50-3(5.7)) \\ f(x_0)=√(50-17.1) \\ f(x_(0)))=√(32.9) \\ f(x_0)=5.736 \end{gathered}`
`\begin{gathered} x_2=f(x_1) \\ f(x_1)=√(50-3x) \\ f(x_1)=√(50-3(5.736)) \\ f(x_1)=5.726 \end{gathered}`
`\begin{gathered} x_3=f(x_2) \\ f(x_2)=√(50-3x) \\ f(x_2)=√(50-3(5.726)) \\ f(x_2)=5.729 \end{gathered}`

Hence,

The final answer is

`\Rightarrow x_3=5.729`

OPTION B is the right answer