I have a math problem I need help with. I tried to do it but I wasn't really sure on any of them, and the last two (d and e) I have no idea how to do.
Question: Which of the following statements about the function y = f(x) graphed here are true and which are false?
Picture of the graph in the textbook(I recreated it as best as I could using Microsoft Paint):
a. lim f(x) does not exist.
My answer for a: False? I wrote "because it does not matter whether or not if the "circle" is shaded in". There is a line going over the part at 2, so I guess it does exist as x-> 2?
b. lim f(x) = 2
My answer for b: true?
c. lim f(x) does not exist
My answer for c: false? The dot is there at 1 so it's false?
d. lim f(x) exists at every point x0 in (-1, 1).
x->x0(x over 0)
My answer for d: I don't understand the question or how to do this
e. lim f(x) exists at every point x0 in (1, 3).
x-> x0(x over 0)
My answer for e: Same as d, don't know.
Any help will be appreciated it, thanks in advance.