6. use the graph of $f(x)=\frac{x}{(x^{2}-2x - 3)^{2}}$ to determine $lim_{x\rightarrow - 1}f(x)$ and…

6. use the graph of $f(x)=\frac{x}{(x^{2}-2x - 3)^{2}}$ to determine $lim_{x\rightarrow - 1}f(x)$ and $lim_{x\rightarrow3}f(x)$.

6. use the graph of $f(x)=\frac{x}{(x^{2}-2x - 3)^{2}}$ to determine $lim_{x\rightarrow - 1}f(x)$ and $lim_{x\rightarrow3}f(x)$.

Answer

Explanation:

Step1: Analyze limit as $x\to - 1$

From the graph, as $x$ approaches - 1 from both the left - hand side and the right - hand side, the function values $y = f(x)$ approach negative infinity. So, $\lim_{x\to - 1}f(x)=-\infty$.

Step2: Analyze limit as $x\to3$

From the graph, as $x$ approaches 3 from both the left - hand side and the right - hand side, the function values $y = f(x)$ approach positive infinity. So, $\lim_{x\to3}f(x)=\infty$.

Answer:

$\lim_{x\to - 1}f(x)=-\infty$, $\lim_{x\to3}f(x)=\infty$