How do you find the asymptotes for # s(t)=(8t)/sin(t)#?

1 Answer
Apr 12, 2016

Answer:

Lines #t=+-kpi#, k = 1, 2, 3, 4,..., parallel to s-axis.

Explanation:

As #t to0_(+-), sto8#.
Here, #0_+-# indicate the approaches for limit, from either side.

As #t to+-kpi_(+-), sto+-oo#, k = 1, 2, 3,...
Here, #kpi_(+-)# indicate the approaches for limit, from either side.

So, the asymptotes are the lines #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.