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"Use the given graph to determine the limit, if it exists.


A coordinate graph is shown with a horizontal line crossing the y-axis at three that ends at the open point 2, 3, a closed point at 2, 1, and another horizontal line starting at the open point 2, -3.


Find limit as x approaches two from the left of f of x. and limit as x approaches two from the right of f of x. "

Use the given graph to determine the limit, if it exists. A coordinate graph is shown with a horizontal line crossing the y-axis at three that ends at the open class=

Verified Answer :

HomertheGenius

\(\lim_{x \to 2} f(x)=3\) ( x approaches 2 from the left )
\(\lim_{x \to 2} f ( x ) = -3\) ( x approaches 2 from the right )

The correct answer is:


The limit of f(x) as x approaches 2 from the left is 3. This is represented algebraically by

\(\lim_{x \to 2} f(x) =3\)

The limit of f(x) as x approaches 2 from the right is -3. This is represented algebraically by

\(\lim_{x \to 2} f(x)=-3\)


Explanation:


From the left, we have a horizontal line approaching the value x=2. When we get to this point, the horizontal line stops at (2, 3). This means the limit is 3.


From the right, we have a horizontal line approaching the value x=2. When we get to this point, the horizontal line stops at (2, -3). This means the limit is -3.

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