Find a formula involving c and h for the local truncation error in the nth step if Euler's method is used

A value of x that satisfies the equation (1+ i)æ³ – 2i = 0 is: Select one: - V2(-1+i) (1+i) (-1+ i) /2(1+i) (1 – i)

8) Use Newton's method to derive the ancient and long standing divide and average method for finding square roots by hand. It is also known as the Babylonian method. √r can be approximated by iterating X¡ +1² (x₁+1=1) using an initial guess x₁. Because √ is the positive solution to the equation x² - r = 0, derive the iterating formula above by simplifying the Newton's method formula using f(x)=x²-r. Note that since r is a constant, d/dx(r) = 0. 9) Use the divide and average method derived in Exercise 8 and modify your code from Exercise 5 (three times) to calculate the square roots of the following numbers to within 8 decimal places (a) r = 2 (b) r = 3 (c) r = 5 You do not need to include all of the code for these problems in the HW you turn in, as most of it will just be the same as number 5. However, write down the first 5 to 8 lines (depending on the language used) that define the function used, the initial guess, and the tolerance, along with the roots found in the end.