https://file.aiquickdraw.com/mathbot/file/1726452602548k3sjz8ep.jpg

The limit problem shown in the image is:

\[
\lim_{{x \to -4}} (7x + 3)
\]

This is a straightforward limit evaluation because the function \( 7x + 3 \) is a linear function, which is continuous everywhere. For continuous functions, the limit as \( x \to a \) is simply the value of the function at \( x = a \).

We can substitute \( x = -4 \) directly into the expression:

\[
7(-4) + 3 = -28 + 3 = -25
\]

Thus, the limit is:

\[
\lim_{{x \to -4}} (7x + 3) = -25
\]

Would you like more details or have any further questions?

Here are 5 related questions for further practice:

1. What is the limit \( \lim_{{x \to 2}} (5x - 4) \)?
2. Evaluate \( \lim_{{x \to 0}} (x^2 - 3x + 1) \).
3. Calculate \( \lim_{{x \to -1}} (2x^2 + 7x + 1) \).
4. What is the limit of \( \lim_{{x \to 3}} (4x - 7) \)?
5. Find \( \lim_{{x \to -5}} (x^3 + 2x^2 - x + 4) \).

**Tip**: For continuous functions, finding the limit at any point is as simple as substituting the point directly into the function.

Find the limit if it exists: \( \lim_{{x \to -4}} (7x + 3) \)

Learn how to evaluate the limit of the linear function 7x + 3 as x approaches -4. This problem demonstrates the application of basic limit laws for continuous functions and is suitable for high school students in Grades 9-12.

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