Answer
a.) true
b.) True
c.) False
d.)False
e.) False
f)True
g) True
Work Step by Step
a.) True, because if you follow along the graph from both the left or the right of x=0, you will end up at the same point.
b.)True, because(0,0) is the same point referred to in part(a)
c.)False, the function itself is equal to 1 where x =1, but the paths of the function lead to (0,0) when approaching from the left or the right.
d.)False, f(x) does not approach 1 from either side of x=1
e)False, F(x) does approach 0 if you come from the right , but it approaches -1 if you come from the left of x=1. The different values means this limit does not exist.
f)True Since(-1,1) is an open interval the non existing limit at x =1 is not included And no other point in that interval has any problems approaching from both sides.
'g.) True The reason stated in part(e)
