For what numbers x, sx 5x, does the graph of y = cot x have vertical asymptotes?

Question

For what numbers x, sx 5x, does the graph of y = cot x have vertical asymptotes? Refer to the graph, which shows y = cot x in blue and y= sin X in red In the interval xs5, what is the smallest value of x for which the graph of y cotx has a vertical asymptote? (Type an exact answer, using as needed. Use integers or fractions for any numbers in the expression. Simplify your answer.) Within the given interval, what is the next x-value for which y cotx has a vertical asymptote? (Type an exact answer, using as needed. Use integers or fractions for any numbers in the expression. Simplify your answer.) At what other x-values in the interval 5xs 5 does the graph of y-cotx have a vertical asymptote? 4x and 5 O There are no others. 3t and 4t O 3%, 4%, and 5

Explanation / Answer

smallest value for which y = cot x has vertical asymptote is

x = pi

next value for which y = cot x has vertical asymptote is

x = 2pi

other x values are

x = 3pi, 4pi . 5pi

3rd option is correct

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