review the graph of function f(x). which statement describes this limit? lim f(x) as x→1 the limit lim f(x)…

review the graph of function f(x). which statement describes this limit? lim f(x) as x→1 the limit lim f(x) as x→1 = ∞ because lim f(x) as x→1⁻ = ∞ and lim f(x) as x→1⁺ = 0 the limit lim f(x) as x→1 does not exist because lim f(x) as x→1 = ∞ and lim f(x) as x→1⁺ = 0 the limit lim f(x) as x→1 does not exist because lim f(x) as x→1 = -∞ and lim f(x) as x→1⁺ = ∞ the limit lim f(x) as x→1 = ∞ because lim f(x) as x→1 = -∞ and lim f(x) as x→1⁻ = ∞

review the graph of function f(x). which statement describes this limit? lim f(x) as x→1 the limit lim f(x) as x→1 = ∞ because lim f(x) as x→1⁻ = ∞ and lim f(x) as x→1⁺ = 0 the limit lim f(x) as x→1 does not exist because lim f(x) as x→1 = ∞ and lim f(x) as x→1⁺ = 0 the limit lim f(x) as x→1 does not exist because lim f(x) as x→1 = -∞ and lim f(x) as x→1⁺ = ∞ the limit lim f(x) as x→1 = ∞ because lim f(x) as x→1 = -∞ and lim f(x) as x→1⁻ = ∞

Answer

Explanation:

Step1: Recall limit - existence condition

The limit $\lim_{x\rightarrow a}f(x)$ exists if and only if $\lim_{x\rightarrow a^{-}}f(x)=\lim_{x\rightarrow a^{+}}f(x)$.

Step2: Analyze left - hand limit

From the graph, as $x$ approaches $1$ from the left ($x\rightarrow1^{-}$), the function values $f(x)$ approach $-\infty$, i.e., $\lim_{x\rightarrow1^{-}}f(x)=-\infty$.

Step3: Analyze right - hand limit

As $x$ approaches $1$ from the right ($x\rightarrow1^{+}$), the function values $f(x)$ approach $\infty$, i.e., $\lim_{x\rightarrow1^{+}}f(x)=\infty$.

Step4: Determine the existence of the limit

Since $\lim_{x\rightarrow1^{-}}f(x)\neq\lim_{x\rightarrow1^{+}}f(x)$, the limit $\lim_{x\rightarrow1}f(x)$ does not exist.

Answer:

The limit $\lim_{x\rightarrow1}f(x)$ does not exist because $\lim_{x\rightarrow1^{-}}f(x)=-\infty$ and $\lim_{x\rightarrow1^{+}}f(x)=\infty$