$$ \lim_{\cdot\rarr3} $$$$ \left(4x-6\right) $$

It looks like you're trying to find the limit of the function $ 4x - 6 $ as $ x $ approaches a certain value, but the limit expression is incomplete.

Let me fill it in and evaluate the limit properly:

\[
\lim_{x \to 3} \left(4x - 6\right)
\]

### Solution
To find this limit, we can substitute $ x = 3 $ directly into the linear function:

\[
\lim_{x \to 3} (4x - 6) = 4(3) - 6 = 12 - 6 = 6
\]

Thus, the value of the limit is:

\[
\lim_{x \to 3} (4x - 6) = 6
\]

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Would you like me to explain why substitution works in this case, or do you have any other questions?

### Related Questions:
1. What is the limit of $ 5x + 2 $ as $ x $ approaches $ 4 $?
2. How do you find the limit of a quadratic function as $ x $ approaches a given value?
3. What is the limit of $ \frac{x^2 - 9}{x - 3} $ as $ x $ approaches $ 3 $?
4. How do you handle limits when substitution results in an indeterminate form?
5. What is the difference between one-sided and two-sided limits?

**Tip:** Direct substitution in limits works when the function is continuous at the point of interest. If not, more advanced techniques like factoring, conjugation, or L'Hôpital's rule may be needed.

The query submitted by the user: $$ \lim_{\cdot \rarr 3} \left(4x - 6\right) $$

Find the limit of the linear function 4x - 6 as x approaches 3. This problem demonstrates the application of the direct substitution method for limits, suitable for high school students in Grades 11-12.

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