Question

The graph of the function F is shown above. What is limF(x)?

Answer 1

4

Step-by-step explanation:

To evaluate a limit, we look at both right and left limi s. If the left and right limits both approach the ssme value, then the limit exists. t

As can be observed from the graph, as we reach x = 2 from the right, the functionseems to reach y = 4. In other other words,

`\lim_(x\to2^+)f(x)=4`

Note the tiny plus sig in the limit . This tells us that we are approaching the limit from the right.

Now let us take a look atthe rleft-hand limit.

Now as we approach x = 2 from the left we see that the function seems to take the value y =4. In other words,

`\lim_(x\to2^-)^f(x)=4.`

Note also the tiny negative sign in the limit. This tells us that we are approaching the limit from the left.

Now both the left and the right-hand limits approach the same value; therefore, the limit exists and its value is the following.

`\boxed{\lim_(x\to2)f(x)=4.}`