Let f be defined as follows, where a ≠ 0, f(x) = { (x^2-2ax+a^2)/x-a if x ≠ a, 5 if x = a

Question

Which of the following are true about f?

I. lim(fx) exists
x --> a
II. f(a) exists
III. f(x) is continuous at x = a

Thank you in advance!

Answer 1

f(x) = (x^2-2ax+a^2)/(x-a) , notice the important bracket I inserted for (x-a)

lim (x^2-2ax+a^2)/(x-a) , as x ---> a
= lim (x-a)^2/(x-a) , as x ---> a
= lim x-a, as x ---> 0
= a-a = 0

draw your conclusions

Answer 2

just consider.
For all x ≠ a, f(x) = x-a