## - Using an Iterative Formula

EXAMPLE
The equation has a root between 3 and 4. Use an iterative process to approximate this root correct to 2 decimal places.

 SOLUTION STEP 1: Make an the subject of the equation. or STEP 2: Choose the approximate equation. (The one which converges). Therefore, we choose since diverges. STEP 3: Rewrite equation as an iterative formula STEP 4: Choose an initial approximation, . (We will choose the midpoint of the interval ) STEP 5: Apply the iterative formula until the desired number of decimal places is attained. Though we only need 2 decimal places, we use more decimal places than required until we get to the final answer. Since , to 2 decimal places is NOT the same as we repeat the iterative process. Since and are BOTH approximately 3.46 to 2 decimal places we can state that the root of the equation between 3 and 4 is approximately 3.46.