The question in the image is written in Indonesian and reads:

1. "Dengan menggunakan Teorema Limit, Hitung Nilai Limit Fungsi Berikut: limit (x→0) (x^3 - 1)"

Translated, it asks:

"Using the Limit Theorem, calculate the limit of the following function as $x \to 0$: $\lim_{{x \to 0}} (x^3 - 1)$"

Solution:

To find $\lim_{{x \to 0}} (x^3 - 1)$:

1. Substitute $x = 0$ directly into the function $f(x) = x^3 - 1$, if the limit exists:

   $f(0) = (0)^3 - 1 = -1$

2. Since $x^3 - 1$ is a polynomial function, it is continuous everywhere, including at $x = 0$. Thus, we can directly substitute $x = 0$ to find the limit.

Conclusion:

$\lim_{{x \to 0}} (x^3 - 1) = -1$

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

Related Questions

1. How do you find limits of functions that result in indeterminate forms?
2. What are the common types of limit theorems used in calculus?
3. How can you evaluate limits for functions that involve division by zero?
4. Why is continuity important in calculating limits?
5. How would the result change if the exponent were different, such as $x^2 - 1$ or $x^4 - 1$?

Tip

For polynomial functions, you can often find limits by direct substitution, as they are continuous on their entire domain.