k(x) is a piecewise function

if k(x)= (x^2-2b+b^2)/(x-b) if x does not equal a

= 5 if x=a

then which of the following is true about k(x):

1) limx->a k(x) exists

2) k(x) is continuous at x=a

3) k(a) exists

so far i think that k(a) will exist because it will equal 5 right? realli not sure about the other two.