Question

use the graph of the function f shown to estimate the indicated quantities to the nearest integer. complete parts a through e. b. find the limit \\( \lim_{x \to 1^+} f(x) \\). select the correct choice below and, if necessary, fill in the answer box to complete your choice. \\( \bigcirc \\) a. \\( \lim_{x \to 1^+} f(x) = \square \\) \\( \bigcirc \\) b. the limit does not exist

Explanation:

Step1: Understand the right - hand limit

To find \(\lim_{x
ightarrow1^{+}}f(x)\), we need to look at the behavior of the function \(f(x)\) as \(x\) approaches \(1\) from the right - hand side (values of \(x\) greater than \(1\)).

Step2: Analyze the graph

From the given graph, as \(x\) approaches \(1\) from the right (moving along the graph towards \(x = 1\) from values like \(x=1.1,x = 1.01\) etc.), we observe the \(y\) - value that the function approaches. By looking at the graph (the blue line and the other parts of the graph), when \(x\) approaches \(1\) from the right, the function approaches a \(y\) - value of \(2\) (after estimating from the grid - like graph).

Answer:

A. \(\lim_{x
ightarrow1^{+}}f(x)=\boxed{2}\)