Limits -- Calculus

Question

Find the limit of the function f(x) = (sqrt(x^2-4x+4)/x-2) as x approaches 2.

Answer 1

f(x) = √(x²-4x+4)/(x-2) = √(x-2)² / (x-2) = ±(x-2)/(x-2) =±1

So lim x→2^- fx)= -1

and lim x→2⁺ f(x) = 1

By the definition of limits, if the left and right limits are not equal, then the limit does not exist.