Question

b. find \\( \lim\limits_{x \to 1^-} f(x) \\). select the correct choice below and, if necessary, fill in the answer box in your choice.\
a. \\( \lim\limits_{x \to 1^-} f(x) = 0 \\) (simplify your answer.)\
\\( \circ \\) b. the limit does not exist.\
find \\( \lim\limits_{x \to 1^+} f(x) \\). select the correct choice below and, if necessary, fill in the answer box in your choice.\
\\( \bullet \\) a. \\( \lim\limits_{x \to 1^+} f(x) = \square \\) (simplify your answer.)

Explanation:

To solve the left - hand limit \(\lim_{x
ightarrow1^{-}}f(x)\) and the right - hand limit \(\lim_{x
ightarrow1^{+}}f(x)\), we need to analyze the behavior of the function \(f(x)\) as \(x\) approaches \(1\) from the left (\(x
ightarrow1^{-}\)) and from the right (\(x
ightarrow1^{+}\)). However, since the graph of the function \(f(x)\) is not provided in the text, we assume that from the given option for the left - hand limit, \(\lim_{x
ightarrow1^{-}}f(x) = 0\) (as option A is marked for the left - hand limit). For the right - hand limit \(\lim_{x
ightarrow1^{+}}f(x)\), we would typically look at the values of \(f(x)\) as \(x\) gets closer to \(1\) from values greater than \(1\). But since the problem seems to be about the limits of a function (a topic in Calculus, a sub - field of Mathematics), and if we assume a common piece - wise function or a function with a certain behavior at \(x = 1\), if the left - hand limit is \(0\) and we assume the right - hand limit has a value (for example, if the function is continuous or has a certain defined behavior), but since the original problem's left - hand limit is given as \(0\) (option A), and for the right - hand limit, if we assume a standard case (but without the graph, we can't be sure, but if we follow the pattern of the left - hand limit), if we assume the function has a limit at \(x = 1\) from the right, and if we take a common example, say \(f(x)\) is a function where as \(x
ightarrow1^{+}\), the limit is also \(0\) (but this is an assumption based on the given left - hand limit option).

For \(\lim_{x

ightarrow1^{-}}f(x)\)

Step 1: Analyze left - hand limit

The left - hand limit \(\lim_{x
ightarrow1^{-}}f(x)\) is the value that \(f(x)\) approaches as \(x\) gets closer to \(1\) from values less than \(1\). From the given options, option A is marked, so \(\lim_{x
ightarrow1^{-}}f(x)=0\)

For \(\lim_{x

ightarrow1^{+}}f(x)\)

Step 1: Analyze right - hand limit

The right - hand limit \(\lim_{x
ightarrow1^{+}}f(x)\) is the value that \(f(x)\) approaches as \(x\) gets closer to \(1\) from values greater than \(1\). If we assume the function has a symmetric or a defined behavior (since the left - hand limit is \(0\) and the problem is likely about a function with a limit at \(x = 1\)), and if we follow the pattern, we assume \(\lim_{x
ightarrow1^{+}}f(x) = 0\) (this is an assumption based on the given left - hand limit and the structure of the problem, in a real - world scenario, we need the graph or the function definition)

Answer:

(for \(\lim_{x
ightarrow1^{-}}f(x)\)): \(0\)