https://r2.erweima.ai/mathbot/image/1725898305866cxn6tkt1.jpg

It seems the text extraction was not accurate due to image clarity. However, from observing the image, it appears the limit expression is:

\[
\lim_{{x \to 2}} \left( 4x^3 - 3x + 8 \right)
\]

Let's solve this limit step-by-step:

1. **Substitute** \(x = 2\) directly into the expression:

\[
4(2)^3 - 3(2) + 8 = 4(8) - 6 + 8
\]

2. **Simplify** the expression:

\[
32 - 6 + 8 = 34
\]

Thus, the limit is:

\[
\boxed{34}
\]

Would you like a deeper explanation of limits, or any other clarifications? 

Here are 5 related questions for practice:
1. What is the limit of \(\lim_{{x \to 3}} (x^2 - 5x + 6)\)?
2. How do we handle limits where direct substitution results in an indeterminate form?
3. What is the limit of a constant function as \(x \to a\)?
4. How can we use L'Hôpital's rule to evaluate limits?
5. What is the difference between one-sided and two-sided limits?

**Tip**: When a limit can be directly substituted, always try that first!

Calculate the limit as x approaches 2 for the expression 4x^3 - 3x + 8.

Explore how to evaluate the limit of the polynomial function 4x^3 - 3x + 8 as x approaches 2 using direct substitution. This problem utilizes fundamental concepts in calculus including limits and polynomial function evaluation.

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