Questions: Compute the values of f(x) = (x-6)/(x-1)^2 in the table to the right and use Complete the table below. x f(x) x f(x) 1.1 -48.9999 0.9 1.01 -498.9999 0.99 1.001 -4999.000 0.999 1.0001 -49999.000 0.9999 (Type integers or decimals.)

Solution Steps

To compute the values of \( f(x) = \frac{x-6}{(x-1)^2} \) for the given \( x \) values, substitute each \( x \) value into the function and evaluate the expression. This will give the corresponding \( f(x) \) values for the table.

Substituting \( x = 0.9 \) into the function \( f(x) = \frac{x-6}{(x-1)^2} \): \[ f(0.9) = \frac{0.9 - 6}{(0.9 - 1)^2} = \frac{-5.1}{0.01} = -510.0000 \]

Substituting \( x = 0.99 \) into the function: \[ f(0.99) = \frac{0.99 - 6}{(0.99 - 1)^2} = \frac{-5.01}{0.0001} = -50099.9999 \]

Substituting \( x = 0.999 \) into the function: \[ f(0.999) = \frac{0.999 - 6}{(0.999 - 1)^2} = \frac{-5.001}{0.000001} = -5000999.9999 \]

Substituting \( x = 0.9999 \) into the function: \[ f(0.9999) = \frac{0.9999 - 6}{(0.9999 - 1)^2} = \frac{-5.0001}{0.00000001} = -500010000.0001 \]

Final Answer