Question

f(x) = {x^2-1 if x doesn't = 1 ; 4 if x equals 1

-which of the following statements are true?
I) the limit of f(x) exists if x approaches 1.
II) f(1) exists
III) f is continuous x=1

Answer 1

I) is true because lim as x --> 1 of f(x) is 0

II) is true because f(1) means f(x) when x = 1, but when x = 1, f(x) = 4. So f(1) = 4, which means it exists

III) is false because there is a removable discontinuity at x=1, another way we can see this is that the limiting value at x=1 is NOT the same as f(1)