To find the right-hand limit of $f(x)$ as $x$ approaches $1$, which is denoted by:

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

we need to know the explicit form of the function $f(x)$. The right-hand limit, $x \to 1^+$, means that we are interested in the value that $f(x)$ approaches as $x$ gets closer to 1 from the right side (i.e., for values of $x$ that are slightly greater than 1).

Steps to Solve:

1. Identify the Function: If you have a specific function $f(x)$, please provide it. This will allow us to determine the behavior of $f(x)$ as $x$ approaches 1 from the right.

2. Compute the Limit: If the function is known, substitute values of $x$ that are slightly greater than 1 (e.g., $x = 1.1, 1.01, 1.001$) into $f(x)$ to observe its behavior as $x$ approaches 1.

3. Analyze the Result: Depending on the function, the limit may exist and be finite, or it may not exist (e.g., it could approach infinity or exhibit oscillatory behavior).

Could you please provide the specific function $f(x)$ for a detailed solution?

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Would you like to see the next steps or have any questions?

Here are 5 related questions to consider:

1. What is the left-hand limit of the same function as $x$ approaches 1?
2. How do you find a two-sided limit?
3. What if $f(x)$ is a piecewise function near $x = 1$?
4. Can a function have different left-hand and right-hand limits?
5. What does it mean if the limit is infinite?

Tip: Always check for continuity at the point where you are finding the limit!