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

Answer

$\operatorname{\lim}_{x\to\pi^{-}}f(x)=\infty$

Vertical asymptote: x = π.

$\lim_{x\to(2\pi)^-}f(x)=-\infty$

Vertical asymptote: x = 2π.

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:

$\operatorname{\lim}_{x\to(2\pi)^{-}}f(x)=-\infty$

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