The expression in the image is:

$\lim_{x \to 3} \sqrt{5x^2 - 2x + 7}$

To solve this, we will evaluate the limit as $x$ approaches 3 by directly substituting $x = 3$ into the expression inside the square root.

Substituting $x = 3$ into the expression:

$5(3)^2 - 2(3) + 7 = 5(9) - 6 + 7 = 45 - 6 + 7 = 46$

Now, the limit becomes:

$\lim_{x \to 3} \sqrt{46} = \sqrt{46}$

Thus, the value of the limit is:

$\sqrt{46}$

Let me know if you want further details or if you have any questions!

Here are 5 relative questions you might consider:

1. What happens if $x$ approaches a different number in this limit?
2. How do we handle limits that result in indeterminate forms, like $\frac{0}{0}$?
3. Can limits involving square roots result in negative numbers?
4. How does L'Hopital's rule apply to limits of more complex expressions?
5. How do you approach limits at infinity?

Tip: When evaluating limits, always check first if direct substitution works before applying more advanced techniques.