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Given that \( L = 5 \) and \( K = 9 \), we can substitute these values into the problem to simplify it.

First, compute the value of \( b \):

\[
b = (-1)^K \cdot (8L + 8) = (-1)^9 \cdot (8 \cdot 5 + 8)
\]
Since \( (-1)^9 = -1 \), we get:

\[
b = -1 \cdot (40 + 8) = -1 \cdot 48 = -48
\]

Now let's address each statement in the question based on the value of \( L = 5 \) and \( K = 9 \):

(a) **Die Funktion \( f \) ist für \( a = 8 \) differenzierbar im Punkt \( x = -(L + 2) \).**
   - Here, \( x = -(5 + 2) = -7 \).
   - The function is said to be differentiable at \( x = -7 \) when \( a = 8 \).
   - We would need to know more about the function \( f \) to determine whether this is true.

(b) **Die Funktion \( f \) ist für \( a = -8 \) nicht differenzierbar im Punkt \( x = -(L + 2) \).**
   - This also refers to the point \( x = -7 \).
   - Similar to (a), determining the truth requires details about \( f \).

(c) **Es gibt kein \( a \in \mathbb{R} \), sodass \( f \) differenzierbar in \( x = -(L + 2) \) ist.**
   - This claims there is no value of \( a \in \mathbb{R} \) such that \( f \) is differentiable at \( x = -7 \).
   - Again, we need information on \( f \) to confirm.

(d) **Die Funktion \( f \) ist nicht differenzierbar in \( x = -1 \).**
   - This statement says that \( f \) is not differentiable at \( x = -1 \).
   - Without the explicit form of \( f \), we cannot verify this.

(e) **\( \lim_{h \to 0} \frac{f(-1+h) - f(-1)}{h} = -8 \).**
   - This limit defines the derivative of \( f \) at \( x = -1 \), claiming the derivative is \( -8 \).
   - The validity depends on the specific function \( f \).

To fully analyze each statement, we need the definition or properties of the function \( f \).

Would you like further details on how to evaluate differentiability in such cases, or how to calculate limits like the one in (e)?

### 5 Related Questions:
1. What are the general criteria for differentiability of a function at a point?
2. How can we determine whether a function is differentiable at a specific point?
3. How does the value of \( b = -48 \) affect the analysis of these statements?
4. What does it mean when the derivative of a function at a point is given as a limit?
5. How can we test if the derivative at a point is equal to a specific value like in (e)?

### Tip:
For limit problems like in part (e), knowing the exact form of the function is crucial to correctly applying the limit definition of the derivative.

Sei b = (-1)^K(8L + 8). Welche der folgenden Aussagen sind richtig, welche falsch? L = 5, K = 9

Evaluate the differentiability of a function f at specific points, including limit calculations. This problem covers key calculus concepts like differentiability and limits, focusing on parameters L = 5, K = 9.

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