Questions: (a) Find the following: i. lim x→-4⁻ f(x) iv. lim x→3⁺ f(x) ii. lim x→-4⁺ f(x) v. lim x→3⁻ f(x) iii. lim x→∞ f(x) vi. lim x→-∞ f(x)

(a) Find the following:
i. lim x→-4⁻ f(x)
iv. lim x→3⁺ f(x)
ii. lim x→-4⁺ f(x)
v. lim x→3⁻ f(x)
iii. lim x→∞ f(x)
vi. lim x→-∞ f(x)
Transcript text: (a) Find the following: i. $\lim _{x \rightarrow-4^{-}} f(x)$ iv. $\lim _{x \rightarrow 3^{+}} f(x)$ ii. $\lim _{x \rightarrow-4^{+}} f(x)$ v. $\lim _{x \rightarrow 3^{-}} f(x)$ iii. $\lim _{x \rightarrow \infty} f(x)$ vi. $\lim _{x \rightarrow-\infty} f(x)$
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Solution

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Solution Steps

Step 1: Identify the limit as x approaches -2 from the left

To find limx2f(x)\lim_{{x \to -2^-}} f(x), observe the behavior of the function as xx approaches 2-2 from the left side. The graph shows that as xx approaches 2-2 from the left, f(x)f(x) approaches ++\infty.

Step 2: Identify the limit as x approaches -2 from the right

To find limx2+f(x)\lim_{{x \to -2^+}} f(x), observe the behavior of the function as xx approaches 2-2 from the right side. The graph shows that as xx approaches 2-2 from the right, f(x)f(x) approaches -\infty.

Step 3: Identify the limit as x approaches 0

To find limx0f(x)\lim_{{x \to 0}} f(x), observe the behavior of the function as xx approaches 00. The graph shows that as xx approaches 00, f(x)f(x) approaches 22.

Final Answer

  1. limx2f(x)=+\lim_{{x \to -2^-}} f(x) = +\infty
  2. limx2+f(x)=\lim_{{x \to -2^+}} f(x) = -\infty
  3. limx0f(x)=2\lim_{{x \to 0}} f(x) = 2
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