Solve lim x→2 of x²

Step-by-step solution

1. $f(x) = x^2$ is a polynomial — polynomials are continuous everywhere.

2. For continuous functions, the limit equals the value: $\lim_{x \to a} f(x) = f(a)$.

3. Substitute $x = 2$: $\lim_{x \to 2} x^2 = 2^2 = 4$.

4. Direct substitution always works for polynomials, rational functions away from zeros of the denominator, and any continuous elementary function.