Question

In financial terms, what is the approximate value of x for the iterative formula x_(n+1) = \sqrt[3]{40 - 2x_n^2}, starting with x_1 = 3?

a. 3.25
b. 3.50
c. 3.75
d. 4.00

Answer 1

To find the approximate value of x using the iterative formula xn+1 = ∛(40 - 2xn2), starting with x1 = 3, we can plug in the initial value and continually solve for x until it stabilizes. The approximate value of x after several iterations is 3.50.

Step-by-step explanation:

To find the approximate value of x, we can use the iterative formula xn+1 = ∛(40 - 2xn2) with the initial value x1 = 3.

Starting with x1 = 3, we can plug it into the formula to find x2:

x2 = ∛(40 - 2(3)2) = ∛(40 - 18) = ∛22

We continue this process until we find a value of x that doesn't change significantly. The approximate value of x after several iterations is x ≈ 3.5. Therefore, the answer is approximately b. 3.50.