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)

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)
Transcript text: Sea $f:[-7,5] \rightarrow \mathbb{R}$ la función cuya gráfica se muestra a continuación: Determine, si existen, los siguientes límites: (a) $\lim _{x \rightarrow-4} f(x)$ (c) $\lim _{x \rightarrow 3} f(x)$ (e) $\lim _{x \rightarrow 1} f(x)$ (g) $\lim _{x \rightarrow-2} f(x)$ (b) $\lim _{x \rightarrow 0} f(x)$ (d) $\lim _{x \rightarrow 1^{-}} f(x)$ (f) $\lim _{x \rightarrow-2^{-}} f(x)$ (h) $\lim _{x \rightarrow-7^{+}} f(x)$
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Solution

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Solution Steps

Step 1: Analyze the limit as x approaches -4

To find \(\lim_{{x \to -4}} f(x)\), observe the behavior of the function as \(x\) approaches \(-4\) from both sides. From the graph, as \(x\) approaches \(-4\) from the left and right, \(f(x)\) approaches 2.

Final Answer

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

Step 2: Analyze the limit as x approaches 0

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 \(-2\).

Final Answer

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

Step 3: Analyze the limit as x approaches 3

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.

Final Answer

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

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