By successive approximations we find that [tex]x \approx 3.3[/tex] for [tex]f(x) = g(x)[/tex].
How to find a solution of two functions by direct inspection
According to the table, the value of [tex]x[/tex] must be between 3 and 3.5. [tex]x[/tex] is the solution of [tex]f(x) = g(x)[/tex] if and only if [tex]f(x) - g(x) = 0[/tex]. Let suppose that [tex]x = 3.3[/tex], then:
[tex]3.3^{2}+13 = 3\cdot (3.3) + 14[/tex]
[tex]-0.01[/tex]
As we need only two decimals, approximation seems to be reasonable.
By successive approximations we find that [tex]x \approx 3.3[/tex] for [tex]f(x) = g(x)[/tex]. [tex]\blacksquare[/tex]
Statement is incomplete and incorrectly formatted, correct form is presented below:
Cora is using successive approximations to estimate a positive solution to [tex]f(x) = g(x)[/tex], where [tex]f(x) = x^{2}+13[/tex] and [tex]g(x) = 3\cdot x + 14[/tex]. The table shows her results for different input values of [tex]x[/tex]:
x f(x) g(x)
0 13 14
1 14 17
2 17 20
3 22 23
4 29 26
3.5 25.25 24.5
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