Questions: Sea f:[-7,5] → ℝ la función cuya gráfica se muestra a continuación: Determine, si existen, los siguientes límites: (a) lim x → -4 f(x) (c) lim x → 3 f(x) (e) lim x → 1 f(x) (g) lim x → -2 f(x) (b) lim x → 0 f(x) (d) lim x → 1^- f(x) (f) lim x → -2^- f(x) (h) lim x → -7^+ f(x)

\[ \lim_{{x \to -4}} f(x) = 2 \]

To find \(\lim_{{x \to 0}} f(x)\), observe the behavior of the function as \(x\) approaches \(0\) from both sides. From the graph, as \(x\) approaches \(0\) from the left and right, \(f(x)\) approaches \(-2\).

\[ \lim_{{x \to 0}} f(x) = -2 \]

To find \(\lim_{{x \to 3}} f(x)\), observe the behavior of the function as \(x\) approaches \(3\) from both sides. From the graph, as \(x\) approaches \(3\) from the left, \(f(x)\) approaches 3, and as \(x\) approaches \(3\) from the right, \(f(x)\) approaches 2. Since the left-hand limit and right-hand limit are not equal, the limit does not exist.

\[ \lim_{{x \to 3}} f(x) \text{ does not exist} \]