7) $lim_{x\rightarrow\frac{pi}{2}^{+}}\tan(x)$
7) $lim_{x\rightarrow\frac{pi}{2}^{+}}\tan(x)$
Answer
Explanation:
Step1: Identify the point of interest on the graph.
We are interested in the behavior of $\tan(x)$ as $x$ approaches $\frac{\pi}{2}$ from the right side. This is denoted as $x \to \frac{\pi}{2}^+$.
Step2: Observe the graph as $x$ approaches $\frac{\pi}{2}$ from the right.
Locate $\frac{\pi}{2}$ on the x-axis. As we approach $\frac{\pi}{2}$ from values slightly greater than $\frac{\pi}{2}$ (i.e., from the right side of $\frac{\pi}{2}$), the graph of $\tan(x)$ goes downwards towards negative infinity. $$ \lim_{x \to \frac{\pi}{2}^+} \tan(x) $$
Step3: Determine the limit.
From the graph, as $x$ approaches $\frac{\pi}{2}$ from the right, the function $\tan(x)$ decreases without bound. $$ \lim_{x \to \frac{\pi}{2}^+} \tan(x) = -\infty $$
Answer:
$$ -\infty $$