Answer:
[tex]f(2.1) = 0.512195[/tex]
[tex]f(2.05) = 0.506173[/tex]
[tex]f(2.01)=0.501247[/tex]
[tex]f(2.001) = 0.500125[/tex]
[tex]f(2.0001) = 0.500012[/tex]
[tex]f(1.9) = 0.487179[/tex]
[tex]f(1.95) = 0.493671[/tex]
[tex]f(1.99) = 0.498747[/tex]
[tex]f(1.999) = 0.499875[/tex]
[tex]f(1.9999) = 0.499987[/tex]
Step-by-step explanation:
Given
[tex]f(x) = \frac{x^2 - 2x}{x^2 - 4}[/tex]
Solve for f(x) for all given values of x
First, we need to simplify f(x)
[tex]f(x) = \frac{x^2 - 2x}{x^2 - 4}[/tex]
[tex]f(x) = \frac{x(x - 2)}{x^2 - 2^2}[/tex]
[tex]f(x) = \frac{x(x - 2)}{(x- 2)(x + 2)}[/tex]
[tex]f(x) = \frac{x}{x + 2}[/tex]
When [tex]x = 2.1[/tex]
[tex]f(x) = \frac{x}{x + 2}[/tex]
[tex]f(2.1) = \frac{2.1}{2.1 + 2}[/tex]
[tex]f(2.1) = \frac{2.1}{4.1}[/tex]
[tex]f(2.1) = 0.512195[/tex]
When [tex]x = 2.05[/tex]
[tex]f(x) = \frac{x}{x + 2}[/tex]
[tex]f(2.05) = \frac{2.05}{2 + 2.05}[/tex]
[tex]f(2.05) = \frac{2.05}{4.05}[/tex]
[tex]f(2.05) = 0.506173[/tex]
When [tex]x = 2.01[/tex]
[tex]f(x) = \frac{x}{x + 2}[/tex]
[tex]f(2.01)=\frac{2.01}{2.01 +2}[/tex]
[tex]f(2.01)=\frac{2.01}{4.01}[/tex]
[tex]f(2.01)=0.501247[/tex]
When [tex]x = 2.001[/tex]
[tex]f(x) = \frac{x}{x + 2}[/tex]
[tex]f(2.001) = \frac{2.001}{2.001 +2}[/tex]
[tex]f(2.001) = \frac{2.001}{4.001}[/tex]
[tex]f(2.001) = 0.500125[/tex]
When [tex]x = 2.0001[/tex]
[tex]f(x) = \frac{x}{x + 2}[/tex]
[tex]f(2.0001) = \frac{2.0001}{2.0001 + 2}[/tex]
[tex]f(2.0001) = \frac{2.0001}{4.0001}[/tex]
[tex]f(2.0001) = 0.500012[/tex]
When [tex]x = 1.9[/tex]
[tex]f(x) = \frac{x}{x + 2}[/tex]
[tex]f(1.9) = \frac{1.9}{1.9 + 2}[/tex]
[tex]f(1.9) = \frac{1.9}{3.9}[/tex]
[tex]f(1.9) = 0.487179[/tex]
When [tex]x = 1.95[/tex]
[tex]f(x) = \frac{x}{x + 2}[/tex]
[tex]f(1.95) = \frac{1.95}{1.95 + 2}[/tex]
[tex]f(1.95) = \frac{1.95}{3.95}[/tex]
[tex]f(1.95) = 0.493671[/tex]
When [tex]x = 1.99[/tex]
[tex]f(x) = \frac{x}{x + 2}[/tex]
[tex]f(1.99) = \frac{1.99}{1.99 + 2}[/tex]
[tex]f(1.99) = \frac{1.99}{3.99}[/tex]
[tex]f(1.99) = 0.498747[/tex]
[tex]f(x) = \frac{x}{x + 2}[/tex]
When [tex]x = 1.999[/tex]
[tex]f(x) = \frac{x}{x + 2}[/tex]
[tex]f(1.999) = \frac{1.999}{1.999 + 2}[/tex]
[tex]f(1.999) = \frac{1.999}{3.999}[/tex]
[tex]f(1.999) = 0.499875[/tex]
When x = 1.9999
[tex]f(x) = \frac{x}{x + 2}[/tex]
[tex]f(1.9999) = \frac{1.9999}{1.9999 + 2}[/tex]
[tex]f(1.9999) = \frac{1.9999}{3.9999}[/tex]
[tex]f(1.9999) = 0.499987[/tex]
Note that all values of f(x) are approximated to 6 decimal places
