For what values of x, if any, does #f(x) = -tan(pi/12-x) # have vertical asymptotes?

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Answer 1 · 2018-01-23T11:12:12

See below.

We recognize that, as:

as #theta-> pi/2color(white)(88888)# , #tan(theta)->oo# ( Undefined )

The function will have vertical asymptotes everywhere it is undefined. i.e. when:

#(pi/12-x)=pi/2#

Solving for #x#:

#x=-pi/2+pi/12=-(5pi)/12#

This will also be true if we add integer multiples of #pi# onto this:

#-(5pi)/12+npi#

For #color(white)(8888)n in ZZ#

GRAPH:

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