https://file.aiquickdraw.com/mathbot/file/1727224737342kda9pc3v.jpg

The expression given is:

\[
\lim_{{x \to 0}} \frac{{x^3 + 2x^2 - 5}}{{x - 1}}
\]

To evaluate this limit, let's plug in \( x = 0 \) directly into the function:

\[
\frac{{0^3 + 2 \cdot 0^2 - 5}}{{0 - 1}} = \frac{{-5}}{{-1}} = 5
\]

Therefore, the value of the limit is:

\[
\lim_{{x \to 0}} \frac{{x^3 + 2x^2 - 5}}{{x - 1}} = 5
\]

If you have any questions or want more details on the calculation, feel free to ask!

**Related Questions:**
1. How do you find the limit of a function as \( x \) approaches a different value?
2. What are some common techniques for evaluating limits involving polynomials?
3. Can you explain L'Hospital's Rule and when it's applicable?
4. How can we find the limit if there is an indeterminate form like \( \frac{0}{0} \)?
5. What is the geometric interpretation of a limit?

**Tip:** When dealing with limits, always check if the function is continuous at the point of interest, and if not, explore techniques like factoring or L'Hospital's Rule to resolve indeterminate forms.

Nilai dari lim_(x -> 0) (x^3 + 2x^2 - 5) / (x - 1)

Learn how to evaluate the limit of the function (x^3 + 2x^2 - 5) / (x - 1) as x approaches 0. The solution involves direct substitution and analysis of polynomials, suitable for students in Grades 10-12.

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