Questions: List any horizontal asymptotes for the following functions. - If there are no asymptotes, enter NONE. - If there is more than one asymptote, give a comma separated list (i.e. 1,2, ...) 1. The function sin(x) has horizontal asymptote(s) y= 2. The function tan^(-1)(x) has horizontal asymptote(s) y=

List any horizontal asymptotes for the following functions.
- If there are no asymptotes, enter NONE.
- If there is more than one asymptote, give a comma separated list (i.e. 1,2, ...)
1. The function sin(x) has horizontal asymptote(s) y=
2. The function tan^(-1)(x) has horizontal asymptote(s) y=

Transcript text: List any horizontal asymptotes for the following functions. - If there are no asymptotes, enter NONE. - If there is more than one asymptote, give a comma separated list (i.e. $1,2, \ldots$ ) 1. The function $\sin (x)$ has horizontal asymptote(s) $y=$ $\square$ 2. The function $\tan ^{-1}(x)$ has horizontal asymptote(s) $y=$ $\square$

Solution

Solution Steps

Step 1: Determine Horizontal Asymptotes for $\sin(x)$

The function $\sin(x)$ is a periodic function with no horizontal asymptotes. It oscillates between -1 and 1 indefinitely.

Final Answer for $\sin(x)$

$\boxed{\text{NONE}}$

Step 2: Determine Horizontal Asymptotes for $\tan^{-1}(x)$

The function $\tan^{-1}(x)$ (also known as $\arctan(x)$) has horizontal asymptotes. As $x \to \infty$, $\tan^{-1}(x) \to \frac{\pi}{2}$, and as $x \to -\infty$, $\tan^{-1}(x) \to -\frac{\pi}{2}$.

Final Answer for $\tan^{-1}(x)$

$\boxed{y = \frac{\pi}{2}, -\frac{\pi}{2}}$

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