Determine the points in the interval ​(1​,6​) at which the function has a discontinuity. At each point of​ discontinuity, state the conditions in the continuity checklist that are violated.
1.​ f(a) is defined​ (a is in the domain of​ f).
2. ModifyingBelow lim With x right arrow alimx→a ​f(x) exists.
3. ModifyingBelow lim With x right arrow a f left parenthesis x right parenthesis equals f left parenthesis a right parenthesislimx→a f(x)=f(a) ​(the value of f equals the limit of f at​ a).

To determine the points of discontinuity of a function within a given interval, we need to check where the function violates one or more conditions from the continuity checklist.

Let's summarize the checklist:

1. **\( f(a) \) is defined** — The function must have a value at the point \( a \), meaning \( a \) is in the domain of the function.
2. **\( \lim_{x \to a} f(x) \) exists** — The limit of the function as \( x \) approaches \( a \) must exist.
3. **\( \lim_{x \to a} f(x) = f(a) \)** — The value of the function at \( a \) must equal the limit of the function as \( x \) approaches \( a \).

### Steps to Identify Points of Discontinuity:

1. **Find the Domain of the Function**: Identify any points within the interval (1,6) where the function is not defined. These would be points where condition (1) is violated.
2. **Check for Limits**: For each point where the function is defined, evaluate whether the left-hand limit \( \lim_{x \to a^-} f(x) \) and the right-hand limit \( \lim_{x \to a^+} f(x) \) exist and are equal. If they are not, then condition (2) is violated.
3. **Check for Function Value Matching the Limit**: If the limit exists, check if \( f(a) = \lim_{x \to a} f(x) \). If not, condition (3) is violated.

To proceed further and analyze the points of discontinuity, I need the **specific function** you're dealing with. Could you provide the function?

Would you like to continue with these steps?

Determine the points in the interval (1,6) at which the function has a discontinuity. At each point of discontinuity, state the conditions in the continuity checklist that are violated.

Learn how to identify points of discontinuity in the interval (1,6) and apply the continuity checklist to determine the violated conditions. This problem covers the concepts of limits, function definitions, and continuity. Suitable for high school students in Grades 10-12.

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