Limits and Continuity

Based on the graph of $f(x)$, as $x$ approaches 2, the y-value approaches 5. Which of the following is the correct limit notation?

From the graph of a function, it is observed that as $x$ approaches 3 from the left, $f(x)$ approaches 2. Which of the following is the correct notation for this observation?

A graph shows that as $x$ approaches 4 from the left, $f(x)$ approaches 7, and as $x$ approaches 4 from the right, $f(x)$ approaches 7. Which of the following statements is true?

Given the following table of values, does $\lim_{x \to 3} f(x)$ exist?

Suppose 1 - x^2 \le f(x) \le 1 + x^2 for all $x$. Find $\lim_{x \to 0} f(x)$.

For the function $f(x) = \begin{cases} x^2, & x \leq 1 \\ ax + b, & x > 1 \end{cases}$, find the values of $a$ and $b$ such that $f(x)$ is continuous and $f(2) = 5$.

Given the limit notation $\lim_{x \to a} f(x) = L$, which of the following statements best describes its meaning?

Given the following table of values for a function $f(x)$, what is the estimated value of $\lim_{x \to 2} f(x)$?

Given that $\lim_{x \to 2} f(x) = 4$ and $\lim_{x \to 2} g(x) = 5$, what is the value of $\lim_{x \to 2} [2f(x) + g(x)]$?

Evaluate $\lim_{x \to 3} \frac{x^2 - 9}{x - 3}$.