Question

The graph of the function f(x) = csc(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

Vertical asymptote: x = π.

`\lim_(x\to(2\pi)^-)f(x)=-\infty`

Vertical asymptote: x = 2π.

Step-by-step explanation

Given the graph of the function

`f(x)=csc(x)`

we can find the limit of the function when x approaches π from the left:

Thus:

`\lim_(x\to\pi^-)f(x)=\infty`

indicating that it has a vertical asymptote at x = π.

Then, we can also find the limit of the function when x approaches 2π from the left:

indicating that it has a vertical asymptote at x = 2π.