Find the vertical asymptotes (if any) of the graph of the function. (Use n as an arbitrary integer if necessary. If an answer does not exist, enter DNE.) s(t) = 5t/sin(t)

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28-04-2017
Mathematics

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Find the vertical asymptotes (if any) of the graph of the function. (Use n as an arbitrary integer if necessary. If an answer does not exist, enter DNE.) s(t) = 5t/sin(t)

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jdoe0001 jdoe0001 · Answer 1 · 2017-04-28T22:52:35+02:00

[tex]\bf s(t)=\cfrac{5t}{sin(t)}[/tex]

a rational expression is asymptotic, when the expression becomes undefined, and that happens when the denominator is 0, or turns to 0

the vertical asymptote is there, only if such value, turns the denominator to 0, whilst not zeroing out the numerator

well, for sine, that is at [tex]\bf -\infty...0,\pi , 2\pi ,3\pi ,4\pi ....+\infty \\\\\\ thus\implies 0\pm \pi n\quad \textit{"n" being an integer}[/tex]