Find the horizontal, vertical and oblique asymptotes of each of the curves.
`{:((a),y=x/(x+4),,(b),y=(x^(2)+4)/(x^(2)-1)),((c),y=x^(3)/(x^(2)+3x-10),,(d),y=(x^(3)+1)/(x^(3)+x)),((e),y=x/(root(4)(x^(4)+1)),,(f),y=(x-9)/(sqrt(4x^(2)+3x+2))),((g),y=1/(2^(x)-1),,(h),y=1/(log_(e) x)),((i),y= 1/(2^(x) - 1),,,):}`

Explanation

To find the horizontal, vertical, and oblique asymptotes for each of the given curves, we will follow a systematic approach. Let's analyze each function step by step.

### (a) \( y = \frac{x}{x+4} \)

1. **Horizontal Asymptote**:
- Find the limit as \( x \) approaches infinity.
\[
\lim_{x \to \infty} \frac{x}{x+4} = \lim_{x \to \infty} \frac{1}{1 + \frac{4}{x}} = 1
...