How do you find the Vertical, Horizontal, and Oblique Asymptote given $s (t) = \frac{8 t}{sin (t)}$ $s(t)=(8t)/sin(t)$ ?

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Answer 1 · 2017-01-05T05:29:18

Vertical: $uarr x = +-kpi darr, k = +-1, +-2, +-3, ...$

As $t to 0, s to 8$ .

$s to +-oo$ , as $t to kpi, k = +-1, +-2, +-3, ...$ , revealing

vertical asymptotes $x=kpi, k = 0, +-1, +-2, +-3, ...$ .

The first graph reveals the trends, for tending towards first pair of

asymptotes $x = +-pi$ .

The second graph seems to say 'Grand New Year!'.

graph{(8x)/sin x [-128.1, 128.3, -64, 64]}

graph{(8x)/sin x [-500,500, -1000, 1000]}

How do you find the Vertical, Horizontal, and Oblique Asymptote given s(t)=(8t)/sin(t)s(t)=8tsin(t)s(t)=(8t)/sin(t)?