Consider the following expression. 7.20 times 10-5 = x(0.100 + x)2 We can solve

Question

Consider the following expression. 7.20 times 10-5 = x(0.100 + x)2 We can solve for x using a technique called successive approximations. If we assume that x is very small compared to 0.100 (such that 0.100 + x = 0.100) then our first approximation of x (let's call it x1) can be calculated as 7.20 times 10-5 = x1 (0.100)2 Now, take your first approximation of x and plug it into the full equation. 7.20 times 10-5 = x2(0.100 + x1)2 Each successive approximation uses the value from the previous approximation. 7.20 times 10-5 = .x3(0.100 + x2)2 etc.: Continue this process until two x values agree within the desired level of precision.

Explanation / Answer

1. x1= 7.2 * 10-5/(0.1)2 = 0.00720

2. x2= 7.2 * 10-5/(0.1+0.0072)2 = 0.00627

3. x3= 7.2 * 10-5/(0.1+0.00627)2 = 0.00638

4. x4= 7.2 * 10-5/(0.1+0.00638)2 = 0.00636

5. x5= 7.2 * 10-5/(0.1+0.00636)2 = 0.00636

6. x3 and x4

7. x4 and x5

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