Answer
A) $\underset{x\to 1}{\mathop{\lim }}\,f\left( x \right)=3$, since, as x approaches 1 the value of $ f\left( x \right)$ gets closer to the y-coordinate of 3.
B) The value of the function $ f\left( 1 \right)$ is 2, thus $ f\left( 1 \right)=2$ .
Work Step by Step
(a)
Consider the provided limit $\underset{x\to 1}{\mathop{\lim }}\,f\left( x \right)$.
To find $\underset{x\to 1}{\mathop{\lim }}\,f\left( x \right)$, examine the portion of the graph near $ x=1$.
As x approaches 1, the value of $ f\left( x \right)$ gets closer to the y-coordinate of 3. This point $\left( 1,3 \right)$ is shown by the open dot in the above graph.
The point $\left( 1,3 \right)$ has the y-coordinate of 3.
Thus, $\underset{x\to 1}{\mathop{\lim }}\,f\left( x \right)=3$.
Hence, the value of $\underset{x\to 1}{\mathop{\lim }}\,f\left( x \right)$ is 3.
(b)
Consider the provided function, $ f\left( 1 \right)$.
To find $ f\left( 1 \right)$, examine the portion of the graph near $ x=1$.
The graph of the function âfâ at $ x=1$ is shown by the open dot in the provided graph with coordinates $\left( 1,2 \right)$.
Thus, $ f\left( 1 \right)=2$.
