complete the sentence below. the negative value k with the greatest value for which x = k is a vertical…
complete the sentence below. the negative value k with the greatest value for which x = k is a vertical asymptote of the graph of y = tan x is (type an exact answer, using π as needed.)
Answer
Explanation:
Step1: Recall tangent - asymptote formula
The vertical asymptotes of (y = \tan x) are given by (x=\frac{\pi}{2}+n\pi), where (n\in\mathbb{Z}) (the set of all integers).
Step2: Find negative (k) value
We want a negative (k) value. Let (x = k=\frac{\pi}{2}+n\pi). To get a negative (k), we set (n=- 1). Then (k=\frac{\pi}{2}+(-1)\pi=\frac{\pi - 2\pi}{2}=-\frac{\pi}{2}).
Answer:
(-\frac{\pi}{2})