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)

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. $\lim _{x \rightarrow-\infty} f(x)$

Solution

Solution Steps

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

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

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

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

Step 3: Identify the limit as x approaches 0

To find $\lim_{{x \to 0}} f(x)$, observe the behavior of the function as $x$ approaches $0$. The graph shows that as $x$ approaches $0$, $f(x)$ approaches $2$.