The given expression is:

\[
\lim_{{x \to 2}} (2x^2 + 3x - 5)
\]

To find this limit, we can simply substitute \( x = 2 \) directly into the expression since it's a polynomial function and is continuous.

1. Substitute \( x = 2 \) into the expression:
   \[
   2(2^2) + 3(2) - 5 = 2(4) + 6 - 5
   \]

2. Simplify:
   \[
   8 + 6 - 5 = 9
   \]

So, the limit is:

\[
\lim_{{x \to 2}} (2x^2 + 3x - 5) = 9
\]

Would you like a detailed explanation of the steps or more examples?

Here are 5 related questions for further practice:
1. What is \(\lim_{{x \to 3}} (4x^2 - 5x + 2)\)?
2. Can you find \(\lim_{{x \to -1}} (x^3 + 2x^2 - 4x + 3)\)?
3. What happens if you have \(\lim_{{x \to 2}} \frac{x^2 - 4}{x - 2}\)?
4. What is the behavior of \(\lim_{{x \to 0}} \frac{\sin(x)}{x}\)?
5. How do you handle \(\lim_{{x \to 1}} \frac{1}{x - 1}\)?

**Tip:** For polynomials, limits at any point can be computed by direct substitution because they are continuous functions.

Learn how to compute the limit of the polynomial function Lim x->2 (2x^2 + 3x - 5) using direct substitution. This step-by-step guide covers key calculus concepts, suitable for students in Grades 10-12.

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