what is the limit as x→7, f(x) = (7x − 2)

To find the limit of the function \( f(x) = 7x - 2 \) as \( x \to 7 \), we can directly substitute \( x = 7 \) into the function since this is a linear expression.

\[
\lim_{{x \to 7}} (7x - 2) = 7(7) - 2 = 49 - 2 = 47
\]

Thus, the limit is:

\[
\lim_{{x \to 7}} f(x) = 47
\]

Would you like more details on this, or do you have any questions?

Here are 5 related questions:
1. What happens if you change the constant term in \( f(x) \)?
2. How would the limit change if the coefficient of \( x \) were different?
3. What if the function were \( f(x) = 7x^2 - 2 \)?
4. How do limits behave for non-linear functions?
5. What is the graphical interpretation of limits?

**Tip:** For simple polynomials or linear functions, limits can often be found by direct substitution, as these functions are continuous everywhere.

Explore how to find the limit of the linear function f(x) = 7x − 2 as x approaches 7. This problem uses direct substitution and introduces key concepts in calculus and limits, suitable for students in Grades 10-12.

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