Find the equations for all vertical asymptotes for the function.
y = csc (5x)
Is this the right answer x= k pi / 5.
To find the equations for the vertical asymptotes of the function y = csc(5x), we need to determine the values of x where the function becomes undefined. Recall that the csc(x) function is defined as the reciprocal of the sin(x) function.
In this case, the csc(5x) function will be undefined whenever sin(5x) is equal to zero, because dividing by zero is undefined. Therefore, we need to solve the equation sin(5x) = 0 to find the vertical asymptotes.
To solve sin(5x) = 0, we can use the fact that sin(x) = 0 when x is a multiple of pi. In other words, sin(x) = 0 when x = n * pi, where n is an integer.
So, for sin(5x) = 0, we can set 5x = n * pi. Dividing both sides by 5 gives us x = (n * pi) / 5, where n is an integer.
Hence, the correct equations for the vertical asymptotes of the function y = csc(5x) are x = n * pi / 5, where n is an integer.
Now, substituting k for n, the correct answer is x = k * pi / 5.