we know that the function f(x) = x^3 is continous at a =-3
find the value of the limit:
lim f(x) as x approaches -3

The function \( f(x) = x^3 \) is a polynomial function, and polynomial functions are continuous everywhere. Since \( f(x) \) is continuous at \( x = -3 \), we can evaluate the limit by direct substitution.

So, we have:

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

Substitute \( x = -3 \) into the function:

\[
f(-3) = (-3)^3 = -27
\]

Therefore, the value of the limit is:

\[
\lim_{{x \to -3}} f(x) = -27
\]

Would you like more details or have any questions?

Here are 5 related questions to consider:

1. What does it mean for a function to be continuous at a point?
2. How would the solution change if \( f(x) = x^2 \) instead of \( x^3 \)?
3. What is the general form of the derivative of \( f(x) = x^n \)?
4. How does the concept of limits relate to the derivative of a function?
5. Can a function be discontinuous but still have a limit at a particular point?

**Tip:** When evaluating limits of continuous functions, you can often directly substitute the value the variable is approaching into the function.

Discover how to evaluate the limit of the function f(x) = x^3 as x approaches -3. This problem explores the concepts of limits, continuity, and polynomial functions, illustrating the direct substitution method. Suitable for high school students in Grades 11-12.

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