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Naddik [55]
3 years ago
7

Evaluate the function f(x) at the given numbers (correct to six decimal places).

Mathematics
1 answer:
3241004551 [841]3 years ago
4 0

Answer:

The function f(x) = \frac{x^{2}-4\cdot x}{x^{2}-16} has the following set of solutions:

f(4.1) = 0.506173, f(4.05) = 0.503106, f(4.01) = 0.500624, f(4.001) = 0.500062, f(4.0001) = 0.500006, f(4.0001) = 0.500006

f(3.9) = 0.493671, f(3.95) = 0.496855, f(3.99) = 0.499374, f(3.999) = 0.499937, f(3.9999) = 0.499994

Step-by-step explanation:

Let be f(x) = \frac{x^{2}-4\cdot x}{x^{2}-16}, we proceed to simplify the expression by Algebraic means:

1) \frac{x^{2}-4\cdot x}{x^{2}-16} Given

2) \frac{x\cdot (x-4)}{(x-4)\cdot (x+4)} Associative, commutative and distributive properties/a^{2}-b^{2} = (a+b)\cdot (a - b)

3) \frac{x}{x + 4} Commutative, associative and modulative properties/Existence of multiplicative inverse/Result

Now we evaluate the function for each value:

x = 4.1

f(4.1) = \frac{4.1}{4.1+4}

f(4.1) = 0.506173

x = 4.05

f(4.05)  = \frac{4.05}{4.05 + 4}

f(4.05) = 0.503106

x = 4.01

f(4.01) = \frac{4.01}{4.01 + 4}

f(4.01) = 0.500624

x = 4.001

f(4.001) = \frac{4.001}{4.001+4}

f(4.001) = 0.500062

x = 4.0001

f(4.0001) = \frac{4.0001}{4.0001 + 4}

f(4.0001) = 0.500006

x = 3.9

f(3.9) = \frac{3.9}{3.9+4}

f(3.9) = 0.493671

x = 3.95

f(3.95) = \frac{3.95}{3.95+4}

f(3.95) = 0.496855

x = 3.99

f(3.99) = \frac{3.99}{3.99+4}

f(3.99) = 0.499374

x = 3.999

f(3.999) = \frac{3.999}{3.999 + 4}

f(3.999) = 0.499937

x = 3.9999

f(3.9999) = \frac{3.9999}{3.9999 + 4}

f(3.9999) = 0.499994

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