Find the x-values at which f is not continuous. Are these discontinuities removable? Find the x-values at which f is not continuous. Are these discontinuities removable.(Use k as an arbitrary integer if needed). f(x) = tan* (πx)/(2)

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You should check if the tangent function is continuous, hence, you need to check if `lim_(x->1, x<1) tan(pi*x/2) = lim_(x->1, x>1) tan(pi*x/2)`  such that:

`lim_(x->1, x<1) tan(pi*x/2) = +oo`

`lim_(x->1, x<1) tan(pi*x/2) = -oo`

Notice that the side limits have no equal values and the function has a vertical asymptote...

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You should check if the tangent function is continuous, hence, you need to check if `lim_(x->1, x<1) tan(pi*x/2) = lim_(x->1, x>1) tan(pi*x/2)`  such that:

`lim_(x->1, x<1) tan(pi*x/2) = +oo`

`lim_(x->1, x<1) tan(pi*x/2) = -oo`

Notice that the side limits have no equal values and the function has a vertical asymptote at `x=1` , hence, the function `f(x) = tan(pi*x/2)` is discontinuous at `x = 1` .

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