Approximate the solution to the equation above using three iterations of successive approximation. Use the graph below as a star
ting point.
2 answers:
Answer:
x ≈ 1.683006
Step-by-step explanation:
There are many successive approximation techniques. For these functions, it seems to work to solve the equation for x:
6^(-x) +4 = 3x -1
6^(-x) +5 = 3x . . . . . . add 1
(6^(-x) +5)/3 = x . . . . divide by the coefficient of x
Then we can use the function ...
f(x) = (6^(-x) +5)/3
to find a new value of x, given an initial value of x.
As we read the graph, the point where the curves cross is at about x=1.7, so that will be our initial starting point for iteration. The attachment shows the successive values of f(x) for three iterations. The third evaluation of f(x) gives an approximate root value of ...
x ≈ 1.683006
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