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The problem asks to find the right-hand limit of the function \( f(x) \) as \( x \) approaches 1 from the positive direction, denoted by:

\[
\lim_{x \to 1^+} f(x)
\]

To solve this using the graph, we examine the behavior of the function as \( x \) approaches 1 from the right (i.e., from values greater than 1). 

Looking at the graph:
- As \( x \to 1^+ \), the function appears to oscillate rapidly near 1 and does not settle on a single value.
- The oscillations increase in magnitude, moving between positive and negative values.

Since the function does not approach a single value but instead oscillates infinitely, the limit does not exist. Therefore:

\[
\lim_{x \to 1^+} f(x) \text{ does not exist (DNE)}.
\]

Would you like more details or have any questions?

Here are some related questions you could explore:
1. What is the definition of a right-hand limit?
2. How can oscillations affect the existence of a limit?
3. What is the difference between a limit existing and approaching infinity?
4. How do we interpret the behavior of a function when it oscillates near a point?
5. Can a function have a limit from the left-hand side and not from the right?

**Tip:** When evaluating limits, always check for oscillatory behavior, which might prevent the limit from existing.

Find the right-hand limit of the function f(x) as x approaches 1 from the positive direction using the graph.

Find the right-hand limit of f(x) as x approaches 1 using a graph. This problem involves key calculus concepts such as limits and oscillations. The solution shows why the limit does not exist based on the graphical behavior of the function.

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