How do you find the asymptotes for $s (t) = \frac{8 t}{sin (t)}$ $s(t)=(8t)/sin(t)$ ?

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How do you find the asymptotes for $s (t) = \frac{8 t}{sin (t)}$ $s(t)=(8t)/sin(t)$ ?

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Answer 1 · 2016-04-12T17:02:08

Lines $t = \pm k π$ $t=+-kpi$ , k = 1, 2, 3, 4,..., parallel to s-axis.

Explanation:

As $t \to 0_{\pm}, s \to 8$ $t to0_(+-), sto8$ .
Here, $0_{\pm}$ $0_+-$ indicate the approaches for limit, from either side.

As $t \to \pm k π_{\pm}, s \to \pm \infty$ $t to+-kpi_(+-), sto+-oo$ , k = 1, 2, 3,...
Here, $k π_{\pm}$ $kpi_(+-)$ indicate the approaches for limit, from either side.

So, the asymptotes are the lines $t = \pm k π$ $t=+-kpi$ , k = 1, 2, 3, 4,..., parallel to s-axis

To understand the approaches fpr limits and limits better, recall that sine is positive in the first two quadrants and negative in the third and fourth.

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How do you find the asymptotes for $s (t) = \frac{8 t}{sin (t)}$ $s(t)=(8t)/sin(t)$ ?

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Explanation:

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How do you find the asymptotes for $s (t) = \frac{8 t}{sin (t)}$ $s(t)=(8t)/sin(t)$ ?