Question

The graph of the function f(x) = sec(x) is given above for the interval x in[0,2 pi] NLY Determine the one-sided limit. Then indicate the equation of the vertical asymptote.

Answer 1

From the given graph, you can conclude that as

`x\rightarrow(\pi)/(2)`

from the right

`f(x)\rightarrow-\infty.`

Therefore:

`\lim_{x\to((\pi)/(2))^+}f(x)=-\infty.`

Also, as

`x\rightarrow(3\pi)/(2)`

from the right

`f(x)\rightarrow\infty.`

Therefore:

`\lim_{x\to((3\pi)/(2))^+}f(x)=\infty.`

Both limits and the graph lead you to conclude that, there are two vertical asymptotes with equations:

`\begin{gathered} x=(\pi)/(2), \\ x=(3\pi)/(2). \end{gathered}`

Answer:

`\begin{gathered} \lim_{x\to((\pi)/(2))^+}f(x)=-\infty, \\ x=(\pi)/(2). \\ \\ \lim_{x\to((3\pi)/(2))^+}f(x)=\infty, \\ x=(3\pi)/(2). \end{gathered}`