Answer:To evaluate the limit of the function (x^2 - 2x) / (x^2 - x - 2) as x approaches 2, we can substitute the given numbers into the function and observe the values.
For the given values: t = 2.5, 2.1, 2.05, 2.01, 2.005, 2.001, 1.9, 1.95, 1.99, 1.995, 1.999
We can calculate the corresponding values of the function:
t = 2.5: (2.5^2 - 2 * 2.5) / (2.5^2 - 2.5 - 2) = (-1.25) / (-0.75) = 1.666667
t = 2.1: (2.1^2 - 2 * 2.1) / (2.1^2 - 2.1 - 2) = (-0.29) / (-0.59) = 0.491525
t = 2.05: (2.05^2 - 2 * 2.05) / (2.05^2 - 2.05 - 2) = (-0.1525) / (-0.1525) = 1
t = 2.01: (2.01^2 - 2 * 2.01) / (2.01^2 - 2.01 - 2) = (-0.0399) / (-0.0399) = 1
t = 2.005: (2.005^2 - 2 * 2.005) / (2.005^2 - 2.005 - 2) = (-0.019975) / (-0.019975) = 1
t = 2.001: (2.001^2 - 2 * 2.001) / (2.001^2 - 2.001 - 2) = (-0.007995) / (-0.007995) = 1
t = 1.9: (1.9^2 - 2 * 1.9) / (1.9^2 - 1.9 - 2) = (0.81) / (0.09) = 9
t = 1.95: (1.95^2 - 2 * 1.95) / (1.95^2 - 1.95 - 2) = (0.4725) / (0.0475) = 9.947368
t = 1.99: (1.99^2 - 2 * 1.99) / (1.99^2 - 1.99 - 2) = (0.0399) / (0.0099) = 4.040404
t = 1.995: (1.995^2 - 2 * 1.995) / (1.995^2 - 1.995 - 2) = (0.019975) / (0.004975) = 4.012048
t = 1.999: (1.999^2 - 2 * 1.999) / (1.999^2 - 1.999 - 2) = (0.007995) / (0.001995) = 4.012531
As we can see from the calculated values, as t approaches 2, the values of the function