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

Answer:

2

Step-by-step explanation:

Let $L$ be a real number.

$\lim_{x \rightarrow 2}f(x)$ equals $L$ if:

$\lim_{x \rightarrow 2^-}f(x)=L$

$\lim_{x \rightarrow 2^+}f(x)=L$

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$\lim_{x \rightarrow 2^-}f(x)$ 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:

$\lim_{x \rightarrow 2^-}f(x)=2$

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$\lim_{x \rightarrow 2^+}f(x)$ 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,

$\lim_{x \rightarrow 2}f(x)=2$.