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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

3. Use the graph below to evaluate the limit as x approaches 2 of f of x : Graph of-example-1
User Trej Gun
by
7.3k points

1 Answer

5 votes

Answer:

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.

3. Use the graph below to evaluate the limit as x approaches 2 of f of x : Graph of-example-1
User Gcamargo
by
8.5k points

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