Final answer:
The vertical asymptotes of the function y = 1/5 cot(3x) are at x = nπ/3, where n is an integer.
Step-by-step explanation:
To find the equations of the vertical asymptotes of the function y = 1/5 cot(3x), we need to understand where the function is undefined. The cotangent function, cot(x), is undefined when its argument, x, is an integer multiple of π because the tangent function, tan(x), has zeroes at these points.
The argument of the cotangent function in our case is 3x. Therefore, we need to find the values of x where 3x is an integer multiple of π. Setting 3x equal to nπ, where n is an integer, we solve for x to get x = nπ/3. These are the points where the function y = 1/5 cot(3x) is undefined, and hence, where the vertical asymptotes are located.
The equations of the vertical asymptotes for the function y = 1/5 cot(3x) are then x = nπ/3, where n is an integer (n = ..., -3, -2, -1, 0, 1, 2, 3, ...).