Question about the calculus

Question

Use the graph of the function f to decide whether the value of the given quantity exists. If it does, find it. If it does not, enter DNE.

(a)

(b)

(c)

(d)

Answer 1

a) f(1) does exist. It is the dot at the point (1, 2). So f(1) = 2

b) Despite the fact that f(1) does exist, the limit as x approaches 1 does NOT exist because as you approach 1 from the left and from the right, you are approaching 2 different numbers. Remember that the limit as you approach a number does not mean you get to the number, in fact, you never get to it, you just keep getting closer and closer. So the limit DNE.

c) f(5) DNE because there is a hole in the graph at the point (5, 2) meaning the function does not have a value there.

d) The limit as you approach 5 does exist and it is 2. Remember again that you never actually get to x = 5 when you take the limit. You just get close and the closer and closer you get to 5, no matter from which direction, the closer and closer you get to a value of 2.