How do you find the Vertical, Horizontal, and Oblique Asymptote given #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]}