Guess the value of the limit by evaluating the function?

Question

I need help, no clue what to do.

Guess the value of the limit by evaluating the function at the given numbers.

lim x^2 - 2x / x^2 - x - 2

x->2

x = 2.5, 2.1, 2.05, 2.01, 2.005, 2.001, 1.9, 1.95, 1.99, 1.995, 1.999

THE ANSWER IS (2/3)

I have no idea how they got that.

please show me how to do it.

Answer 1

The decimal equivalent of 2/3 is 0.66666666666.... If you plug in the numbers given into the equation, the answer gets closer and closer to 0.66666666... as the number you plug in gets closer to 2. Try the two values closest to 2 in the list: 2.001 and 1.999. The answer is darn close to 0.666666...