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The equation given is:

\[
\lim_{x \to 2} (x^2 + 4x) = 12.
\]

We are tasked with verifying or solving this limit equation.

### Step 1: Substitute \( x = 2 \) into the expression

We need to check if substituting \( x = 2 \) into the expression results in the value 12:

\[
x^2 + 4x = (2)^2 + 4(2) = 4 + 8 = 12.
\]

This matches the right-hand side of the equation, so the limit holds.

Thus, we have:

\[
\lim_{x \to 2} (x^2 + 4x) = 12.


Learn how to solve the limit problem lim_{x \to 2}(x^2 + 4x) = 12 with a clear step-by-step solution. This tutorial covers the concepts of algebraic substitution and limit theorems, appropriate for students in Grades 10-12.

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