Update README.md

README.md

@@ -95,7 +95,49 @@ inputs = tokenizer(
 text_streamer = TextStreamer(tokenizer)
 _ = model.generate(**inputs, streamer=text_streamer, max_new_tokens=2000)
 ```
+```python
+<s> Provide a helpful and informative response to the following prompt.
+
+### Prompt:
+Explain the concept of limits in calculus and their importance. Provide an example of how limits are used to define other calculus concepts.
+
+### Response:
+<thinking>
+1. To begin, I'll identify the key concepts involved in the question. Limits are mathematical concepts that describe the behavior of a function as it approaches a specific value or limit. The question is asking about the importance of limits in calculus, which implies that I need to understand the significance of limits in the context of calculus.
+
+2. To better understand the concept of limits, I'll break it down into smaller sub-questions:
+  a. What are the types of limits that can be defined in calculus?
+  b. How do limits relate to the concept of continuity?
+  c. What are the limitations of limits in calculus?
+
+3. Let's explore each sub-question in detail:
+  a. Types of limits: There are several types of limits that can be defined in calculus, including:
+     i. Limit of a function at a point (e.g., the limit of a function at a point with a specific value).
+     ii. Limit of a function at a sequence (e.g., the limit of a function at a sequence of points).
+     iii. Limit of a function at a limit (e.g., the limit of a function at a limit).
+
+  b. Relationship between limits and continuity: Limits are related to continuity in calculus. Continuity is the property of a function to be continuous everywhere. Limits are used to define the limits of functions at points where continuity is not continuous.
 
+  c. Limits limitations: Limits can be difficult to define in calculus due to the complexity of the function and the difficulty of finding a unique limit. This is because limits are defined by the limiting behavior of the function at the limit. However, there are some simplifications that can be made. For example, if the function is continuous at a point, then the limit of the function at that point is the limit of the function at the point.
+
+4. Now, I'll integrate the insights from the sub-questions to form a coherent answer:
+  The concept of limits is crucial in calculus because it allows us to define the limits of functions at points where continuity is not continuous. Limits are used to define the limits of functions at points where continuity is not continuous. This is because limits are defined by the limiting behavior of the function at the limit.
+
+</thinking>
+
+<preoutput>
+The concept of limits is crucial in calculus because it allows us to define the limits of functions at points where continuity is not continuous. Limits are used to define the limits of functions at points where continuity is not continuous. This is because limits are defined by the limiting behavior of the function at the limit.
+</preoutput>
+
+<checking>
+Upon reviewing my response, I noticed that I didn't provide a specific example of how limits are used to define other calculus concepts. To improve my answer, I can provide an example of how limits are used to define the derivative of a function.
+
+</checking>
+
+<output>
+The concept of limits is crucial in calculus because it allows us to define the derivatives of functions at points where continuity is not continuous. Limits are used to define the derivatives of functions at points where continuity is not continuous. This is because limits are defined by the limiting behavior of the function at the limit. For example, if the function is continuous at a point, then the derivative of the function at that point is the limit of the function at the point.
+</output></s>
+```
 ## **Model Details**
 
 - **Developed By**: Terrance Craddock