George is solving the equation below by finding successive approximations. He started from a graph where he found the solution t
o be between 5 and 6. Using the lower and upper bounds from the graph, George did the following work for the first iteration. Step 1 Rewrite the equation so that it equals zero. Step 2 Evaluate the rewritten equation at the lower and upper bounds. Since the solution to the original equation is represented by a zero, one of the bounds should yield a negative difference and the other should yield a positive difference. Step 3 Take the average of the lower and upper bounds from the graph. Step 4 Evaluate the rewritten equation at . Step 5 Since this value of x yields a negative difference, use it to replace the previous upper bound that yielded a negative difference, . So, the bounds are now and . In what step, if any, did George make his first mistake? A. In step 1, George should have subtracted in the opposite order to set the equation equal to 0. B. In step 5, George should have used as the new lower bound. C. George made no mistakes, and his work is correct. D. In step 3, George should have averaged the two differences instead of the two bounds.
The mistake made by George is; D:George should have averaged the two differences instead of the two bounds.
<h3>How to Solve Successive Approximations?</h3>
In Mathematics, successive approximation can be defined as a classical method that is used in Calculus for solving integral equations or initial value problems.
In this question, George started the first iteration of successive approximation by using the lower and upper bounds of the graph. However, we can deduce that George made a mistake instep 5 because he should have used x = 3/2 as the new upper bound.
