Question

3.

Use the graph below to evaluate the limit as x approaches 2 of f of x :

Graph of a function that increases for x greater than or equal to 0 and less than 2 and decreases for x greater than 2 and less than or equal to 4. The point (2, 3) is marked on the graph (5 points)


0

2

3

4

Answer 1

2

Explanation:

Let
`L` be a real number.

`\lim_(x \rightarrow 2)f(x)` equals
`L` if:

`\lim_(x \rightarrow 2^-)f(x)=L`

`\lim_(x \rightarrow 2^+)f(x)=L`

----------------------------

`\lim_(x \rightarrow 2^-)f(x)` means what does
`y` get close to as we move
`x` closer to 2 from the left. Please look at the orange to see what that looks like visually.

We see that
`y` tends to
`2`.

This means:

`\lim_(x \rightarrow 2^-)f(x)=2`

-----------------------------

`\lim_(x \rightarrow 2^+)f(x)` means what does
`y` get close to as we move
`x` closer to 2 from the right. Please look at the blue to see what that looks like visually.

We see that
`y` tends to
`2`.

This means:

`\lim_(x \rightarrow 2^+)f(x)=2`

----------------------------

Therefore,

`\lim_(x \rightarrow 2)f(x)=2`.