F(X)=9 csc6(X)
it is continous from -infity to infinity except what value?
To determine where the function F(x) = 9csc6(x) is not continuous, we need to look for values of x where the function is undefined or has a discontinuity.
First, let's break down the function. The csc(x) function is the reciprocal of the sin(x) function. Therefore, csc(x) is undefined when sin(x) is equal to zero because division by zero is undefined.
In this case, we have F(x) = 9csc6(x). The argument of the csc function is 6(x), so we need to find where sin(6x) is equal to zero.
The sin(x) function is equal to zero at an infinite number of values since it is a periodic function. The general form of x for which sin(x) is equal to zero is x = nπ, where n is an integer.
Applying this to our case, we get sin(6x) = 0 when 6x = nπ, where n is an integer. Rearranging the equation, x = nπ/6.
In other words, the function F(x) = 9csc6(x) is discontinuous for values of x that satisfy x = nπ/6, where n is an integer.
Therefore, the function F(x) = 9csc6(x) is continuous for all real numbers except x = nπ/6, where n is an integer.