Question

b) $lim_{x
ightarrow(\frac{pi}{2})^{-}}\tan x$

Explanation:

Step1: Recall the definition of tangent function

$\tan x=\frac{\sin x}{\cos x}$

Step2: Analyze the limit as $x\to(\frac{\pi}{2})^{-}$

As $x\to(\frac{\pi}{2})^{-}$, $\sin x\to1$ and $\cos x\to0^{+}$.

Step3: Determine the value of the limit

Since $\tan x = \frac{\sin x}{\cos x}$, and $\sin x\to1$, $\cos x\to0^{+}$ as $x\to(\frac{\pi}{2})^{-}$, then $\lim_{x\to(\frac{\pi}{2})^{-}}\tan x=+\infty$

Answer:

$+\infty$