Question

Select the correct location on the table. Consider the following equations. f(x)= (x^2+3x+2)/(x+8) and g(x)= (x-1)/x. Approximate the solution to the equation f(x)=g(x) using three iterations of successive approximation. Use the graph as a starting point. Select the approximate value for the solution to the equation in the table below. NO LINKS!!
Successive Approximation Intersection Values

-63/16. | -31/8
-61/16. |. -15/4
-59/16. |. -29/8​

Answer 1

Answer:

  (b)  -61/16 | -15/4

Step-by-step explanation:

We assume you're using a binary search successive approximation technique that starts with an interval and cuts it in half with each iteration. The final approximation of the solution to the equation will be the midpoint of the interval after it has been cut in half 3 times.

The graph shows the intersection point of the curves lies between x = -4 and x = -3.

If we define h(x) = f(x) -g(x), then our first iteration will evaluate h(-7/2) and determine which end of the interval gets replaced. The attachment shows us that the sign of h(-7/2) is the same as the sign of h(-3), so -7/2 replaces -3 and the interval after the first iteration is [-4, -7/2].

The midpoint of this interval is -15/4. The sign of h(-15/4) is the same as the sign of h(-7/2), so the interval after the second iteration is [-4, -15/4].

The midpoint of this interval is -31/8. The sign of h(-31/8) is the same as the sign of h(-4), so the interval containing the solution after the third iteration is [-31/8, -15/4]. The approximate solution value after 3 iterations is (-31/8 -15/4)/2 = -61/16.

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