1. **Problem:** Evaluate the limit of the function $f(x) = x^2 + 3x + 2$ as $x$ approaches 1. 2. **Formula and rule:** For polynomial functions, the limit as $x$ approaches a value $a$ is simply the value of the function at $a$, i.e., $\lim_{x \to a} f(x) = f(a)$. 3. **Calculation:** Substitute $x = 1$ into the function: $$f(1) = 1^2 + 3(1) + 2 = 1 + 3 + 2 = 6$$ 4. **Answer:** The limit of $f(x)$ as $x$ approaches 1 is 6. 1. **Problem:** Evaluate the limit of the function $f(x) = 2x^2 - 5x + 1$ as $x$ approaches 2. 2. **Formula and rule:** Again, for polynomial functions, the limit as $x$ approaches $a$ is $f(a)$. 3. **Calculation:** Substitute $x = 2$ into the function: $$f(2) = 2(2)^2 - 5(2) + 1 = 2(4) - 10 + 1 = 8 - 10 + 1 = -1$$ 4. **Answer:** The limit of $f(x)$ as $x$ approaches 2 is -1.