Answer:
The function [tex]f(x) = \frac{x^{2}-4\cdot x}{x^{2}-16}[/tex] has the following set of solutions:
[tex]f(4.1) = 0.506173[/tex], [tex]f(4.05) = 0.503106[/tex], [tex]f(4.01) = 0.500624[/tex], [tex]f(4.001) = 0.500062[/tex], [tex]f(4.0001) = 0.500006[/tex], [tex]f(4.0001) = 0.500006[/tex]
[tex]f(3.9) = 0.493671[/tex], [tex]f(3.95) = 0.496855[/tex], [tex]f(3.99) = 0.499374[/tex], [tex]f(3.999) = 0.499937[/tex], [tex]f(3.9999) = 0.499994[/tex]
Step-by-step explanation:
Let be [tex]f(x) = \frac{x^{2}-4\cdot x}{x^{2}-16}[/tex], we proceed to simplify the expression by Algebraic means:
1) [tex]\frac{x^{2}-4\cdot x}{x^{2}-16}[/tex] Given
2) [tex]\frac{x\cdot (x-4)}{(x-4)\cdot (x+4)}[/tex] Associative, commutative and distributive properties/[tex]a^{2}-b^{2} = (a+b)\cdot (a - b)[/tex]
3) [tex]\frac{x}{x + 4}[/tex] Commutative, associative and modulative properties/Existence of multiplicative inverse/Result
Now we evaluate the function for each value:
[tex]x = 4.1[/tex]
[tex]f(4.1) = \frac{4.1}{4.1+4}[/tex]
[tex]f(4.1) = 0.506173[/tex]
[tex]x = 4.05[/tex]
[tex]f(4.05) = \frac{4.05}{4.05 + 4}[/tex]
[tex]f(4.05) = 0.503106[/tex]
[tex]x = 4.01[/tex]
[tex]f(4.01) = \frac{4.01}{4.01 + 4}[/tex]
[tex]f(4.01) = 0.500624[/tex]
[tex]x = 4.001[/tex]
[tex]f(4.001) = \frac{4.001}{4.001+4}[/tex]
[tex]f(4.001) = 0.500062[/tex]
[tex]x = 4.0001[/tex]
[tex]f(4.0001) = \frac{4.0001}{4.0001 + 4}[/tex]
[tex]f(4.0001) = 0.500006[/tex]
[tex]x = 3.9[/tex]
[tex]f(3.9) = \frac{3.9}{3.9+4}[/tex]
[tex]f(3.9) = 0.493671[/tex]
[tex]x = 3.95[/tex]
[tex]f(3.95) = \frac{3.95}{3.95+4}[/tex]
[tex]f(3.95) = 0.496855[/tex]
[tex]x = 3.99[/tex]
[tex]f(3.99) = \frac{3.99}{3.99+4}[/tex]
[tex]f(3.99) = 0.499374[/tex]
[tex]x = 3.999[/tex]
[tex]f(3.999) = \frac{3.999}{3.999 + 4}[/tex]
[tex]f(3.999) = 0.499937[/tex]
[tex]x = 3.9999[/tex]
[tex]f(3.9999) = \frac{3.9999}{3.9999 + 4}[/tex]
[tex]f(3.9999) = 0.499994[/tex]
