For what values of x, if any, does #f(x) = 1/((x^2-4)cos(pi/2+(7pi)/x) # have vertical asymptotes?

1 Answer

Answer:

#x = +-2, +-7( 1, 1/2, 1/3, 1/4, ...)#

Explanation:

The vertical asymptotes are given by

zero of #x^2-4=0# and #cos(pi/2+7/xpi)=0 => -sin(7pi/x)#.

These are

#x = +-2# and #7/k, k = +-1, +-2, +-3, ...#

Note that k = 0 sends #x to +-oo# to make kx read 7 .

The ad hoc graph is not to scale.
graph{-1/((x^2-4)sin(21.991/x) [-3.51, 3.47, -17, 17]}