when referring to limits and direct substitution, what do L and K mean?

When discussing limits and direct substitution in calculus, the symbols **L** and **K** typically represent the following:

1. **L**: This represents the value that the function approaches as the input (or variable) approaches a particular point. Formally, if we say \(\lim_{x \to a} f(x) = L\), it means that as \(x\) gets closer and closer to \(a\), the function \(f(x)\) gets closer and closer to \(L\).

2. **K**: This is often used to represent a specific constant value, such as the value of the function at the point \(x = a\). When directly substituting, \(K\) might represent \(f(a)\), which is the function's value when you directly substitute \(a\) into \(f(x)\).

In summary:
- **L** represents the limit (the value that \(f(x)\) approaches as \(x\) approaches a certain point).
- **K** represents the constant value of the function at a specific point, particularly when direct substitution is possible (i.e., \(f(a)\)).

Would you like more details on limits or substitution?

### Related Questions:
1. What are the conditions under which direct substitution can be used to find limits?
2. What happens when direct substitution results in an indeterminate form?
3. How do you interpret the limit when \(L \neq K\)?
4. Can \(L\) be infinite? What does that imply?
5. What are the common techniques for evaluating limits when direct substitution doesn’t work?

**Tip**: When evaluating limits, always check if the function is continuous at the point before using direct substitution.

When referring to limits and direct substitution, what do L and K mean?

Explore the concepts of limits and direct substitution in calculus, focusing on the meaning of L and K. Learn how L represents the limit of a function as it approaches a point, while K stands for the constant value of the function at that point. Suitable for students in Grades 11-12.

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